Algebra Examples

$4 (x + 2) {(8 x + 7)}^{3} {(x + 2)}^{5}$

Write $4 (x + 2) {(8 x + 7)}^{3} {(x + 2)}^{5}$ as a function.

$f (x) = 4 (x + 2) {(8 x + 7)}^{3} {(x + 2)}^{5}$

Identify the degree of the function.

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Simplify and reorder the polynomial.

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Multiply $x + 2$ by ${(x + 2)}^{5}$ by adding the exponents.

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Move ${(x + 2)}^{5}$ .

$4 ({(x + 2)}^{5} (x + 2)) {(8 x + 7)}^{3}$

Multiply ${(x + 2)}^{5}$ by $x + 2$ .

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Raise $x + 2$ to the power of $1$ .

$4 ({(x + 2)}^{5} {(x + 2)}^{1}) {(8 x + 7)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 {(x + 2)}^{5 + 1} {(8 x + 7)}^{3}$

Add $5$ and $1$ .

$4 {(x + 2)}^{6} {(8 x + 7)}^{3}$

Use the Binomial Theorem.

$4 (x^{6} + 6 x^{5} \cdot 2 + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Simplify terms.

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Simplify each term.

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Multiply $2$ by $6$ .

$4 (x^{6} + 12 x^{5} + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $2$ .

$4 (x^{6} + 12 x^{5} + 15 x^{4} \cdot 4 + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $4$ by $15$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $3$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 8 + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $8$ by $20$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $4$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 16 + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $16$ by $15$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $5$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 32 + 2^{6}) {(8 x + 7)}^{3}$

Multiply $32$ by $6$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $6$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 64) {(8 x + 7)}^{3}$

Apply the distributive property.

$(4 x^{6} + 4 (12 x^{5}) + 4 (60 x^{4}) + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Simplify.

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Multiply $12$ by $4$ .

$(4 x^{6} + 48 x^{5} + 4 (60 x^{4}) + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $60$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $160$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $240$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $192$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $4$ by $64$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) {(8 x + 7)}^{3}$

Use the Binomial Theorem.

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) ({(8 x)}^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Simplify each term.

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Apply the product rule to $8 x$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (8^{3} x^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Raise $8$ to the power of $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Apply the product rule to $8 x$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 (8^{2} x^{2}) \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Raise $8$ to the power of $2$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 (64 x^{2}) \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $64$ by $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 192 x^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $7$ by $192$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $8$ by $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 24 x \cdot 7^{2} + 7^{3})$

Raise $7$ to the power of $2$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 24 x \cdot 49 + 7^{3})$

Multiply $49$ by $24$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 1176 x + 7^{3})$

Raise $7$ to the power of $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 1176 x + 343)$

Expand $(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 1176 x + 343)$ by multiplying each term in the first expression by each term in the second expression.

$4 x^{6} (512 x^{3}) + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Simplify terms.

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Simplify each term.

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Rewrite using the commutative property of multiplication.

$4 \cdot 512 x^{6} x^{3} + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$4 \cdot 512 (x^{3} x^{6}) + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 \cdot 512 x^{3 + 6} + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $6$ .

$4 \cdot 512 x^{9} + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $4$ by $512$ .

$2048 x^{9} + 4 x^{6} (1344 x^{2}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 4 \cdot 1344 x^{6} x^{2} + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 4 \cdot 1344 (x^{2} x^{6}) + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 4 \cdot 1344 x^{2 + 6} + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $6$ .

$2048 x^{9} + 4 \cdot 1344 x^{8} + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $4$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4 x^{6} (1176 x) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4 \cdot 1176 x^{6} x + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{6}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4 \cdot 1176 (x \cdot x^{6}) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{6}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4 \cdot 1176 (x^{1} x^{6}) + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4 \cdot 1176 x^{1 + 6} + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $6$ .

$2048 x^{9} + 5376 x^{8} + 4 \cdot 1176 x^{7} + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $4$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 4 x^{6} \cdot 343 + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $4$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 48 x^{5} (512 x^{3}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 48 \cdot 512 x^{5} x^{3} + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 48 \cdot 512 (x^{3} x^{5}) + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 48 \cdot 512 x^{3 + 5} + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $5$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 48 \cdot 512 x^{8} + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $48$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 48 x^{5} (1344 x^{2}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 48 \cdot 1344 x^{5} x^{2} + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 48 \cdot 1344 (x^{2} x^{5}) + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 48 \cdot 1344 x^{2 + 5} + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $5$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 48 \cdot 1344 x^{7} + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $48$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 x^{5} (1176 x) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 \cdot 1176 x^{5} x + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{5}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 \cdot 1176 (x \cdot x^{5}) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{5}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 \cdot 1176 (x^{1} x^{5}) + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 \cdot 1176 x^{1 + 5} + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $5$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 48 \cdot 1176 x^{6} + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $48$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 48 x^{5} \cdot 343 + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $48$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 240 x^{4} (512 x^{3}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 240 \cdot 512 x^{4} x^{3} + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 240 \cdot 512 (x^{3} x^{4}) + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 240 \cdot 512 x^{3 + 4} + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $4$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 240 \cdot 512 x^{7} + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $240$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 240 x^{4} (1344 x^{2}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 240 \cdot 1344 x^{4} x^{2} + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 240 \cdot 1344 (x^{2} x^{4}) + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 240 \cdot 1344 x^{2 + 4} + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $4$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 240 \cdot 1344 x^{6} + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $240$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 x^{4} (1176 x) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 \cdot 1176 x^{4} x + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{4}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 \cdot 1176 (x \cdot x^{4}) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{4}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 \cdot 1176 (x^{1} x^{4}) + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 \cdot 1176 x^{1 + 4} + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $4$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 240 \cdot 1176 x^{5} + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $240$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 240 x^{4} \cdot 343 + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $240$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 640 x^{3} (512 x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 640 \cdot 512 x^{3} x^{3} + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 640 \cdot 512 (x^{3} x^{3}) + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 640 \cdot 512 x^{3 + 3} + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $3$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 640 \cdot 512 x^{6} + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $640$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 x^{3} (1344 x^{2}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 x^{3} x^{2} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 (x^{2} x^{3}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 x^{2 + 3} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $3$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 x^{5} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $640$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{3} x + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 (x \cdot x^{3}) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{3}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 (x^{1} x^{3}) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{1 + 3} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $3$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{4} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $640$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $640$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{2} x^{3} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 (x^{3} x^{2}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{3 + 2} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{5} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{2} x^{2} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 (x^{2} x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{2 + 2} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{4} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{2} x + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 (x \cdot x^{2}) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{2}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 (x^{1} x^{2}) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{1 + 2} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{3} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $960$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x \cdot x^{3} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 (x^{3} x) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 (x^{3} x^{1}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x^{3 + 1} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x^{4} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x \cdot x^{2} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 (x^{2} x) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 (x^{2} x^{1}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x^{2 + 1} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x^{3} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 x \cdot x + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 (x \cdot x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 x^{2} + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $768$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $512$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $1344$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 256 (1176 x) + 256 \cdot 343$

Multiply $1176$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 256 \cdot 343$

Multiply $256$ by $343$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Simplify by adding terms.

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Add $5376 x^{8}$ and $24576 x^{8}$ .

$2048 x^{9} + 29952 x^{8} + 4704 x^{7} + 1372 x^{6} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $4704 x^{7}$ and $64512 x^{7}$ .

$2048 x^{9} + 29952 x^{8} + 69216 x^{7} + 1372 x^{6} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $69216 x^{7}$ and $122880 x^{7}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 1372 x^{6} + 56448 x^{6} + 16464 x^{5} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $1372 x^{6}$ and $56448 x^{6}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 57820 x^{6} + 16464 x^{5} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $57820 x^{6}$ and $322560 x^{6}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 380380 x^{6} + 16464 x^{5} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $380380 x^{6}$ and $327680 x^{6}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 16464 x^{5} + 282240 x^{5} + 82320 x^{4} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $16464 x^{5}$ and $282240 x^{5}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 298704 x^{5} + 82320 x^{4} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $298704 x^{5}$ and $860160 x^{5}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1158864 x^{5} + 82320 x^{4} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $1158864 x^{5}$ and $491520 x^{5}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 82320 x^{4} + 752640 x^{4} + 219520 x^{3} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $82320 x^{4}$ and $752640 x^{4}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 834960 x^{4} + 219520 x^{3} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $834960 x^{4}$ and $1290240 x^{4}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2125200 x^{4} + 219520 x^{3} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $2125200 x^{4}$ and $393216 x^{4}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 219520 x^{3} + 1128960 x^{3} + 329280 x^{2} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $219520 x^{3}$ and $1128960 x^{3}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 1348480 x^{3} + 329280 x^{2} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $1348480 x^{3}$ and $1032192 x^{3}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2380672 x^{3} + 329280 x^{2} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $2380672 x^{3}$ and $131072 x^{3}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 329280 x^{2} + 903168 x^{2} + 263424 x + 344064 x^{2} + 301056 x + 87808$

Add $329280 x^{2}$ and $903168 x^{2}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1232448 x^{2} + 263424 x + 344064 x^{2} + 301056 x + 87808$

Add $1232448 x^{2}$ and $344064 x^{2}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1576512 x^{2} + 263424 x + 301056 x + 87808$

Add $263424 x$ and $301056 x$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1576512 x^{2} + 564480 x + 87808$

The largest exponent is the degree of the polynomial.

$9$

Since the degree is odd, the ends of the function will point in the opposite directions.

Odd

Identify the leading coefficient.

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Simplify the polynomial, then reorder it left to right starting with the highest degree term.

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Multiply $x + 2$ by ${(x + 2)}^{5}$ by adding the exponents.

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Move ${(x + 2)}^{5}$ .

$4 ({(x + 2)}^{5} (x + 2)) {(8 x + 7)}^{3}$

Multiply ${(x + 2)}^{5}$ by $x + 2$ .

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Raise $x + 2$ to the power of $1$ .

$4 ({(x + 2)}^{5} {(x + 2)}^{1}) {(8 x + 7)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 {(x + 2)}^{5 + 1} {(8 x + 7)}^{3}$

Add $5$ and $1$ .

$4 {(x + 2)}^{6} {(8 x + 7)}^{3}$

Use the Binomial Theorem.

$4 (x^{6} + 6 x^{5} \cdot 2 + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Simplify terms.

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Simplify each term.

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Multiply $2$ by $6$ .

$4 (x^{6} + 12 x^{5} + 15 x^{4} \cdot 2^{2} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $2$ .

$4 (x^{6} + 12 x^{5} + 15 x^{4} \cdot 4 + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $4$ by $15$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 2^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $3$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 20 x^{3} \cdot 8 + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $8$ by $20$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 2^{4} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $4$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 15 x^{2} \cdot 16 + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Multiply $16$ by $15$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 2^{5} + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $5$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 6 x \cdot 32 + 2^{6}) {(8 x + 7)}^{3}$

Multiply $32$ by $6$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 2^{6}) {(8 x + 7)}^{3}$

Raise $2$ to the power of $6$ .

$4 (x^{6} + 12 x^{5} + 60 x^{4} + 160 x^{3} + 240 x^{2} + 192 x + 64) {(8 x + 7)}^{3}$

Apply the distributive property.

$(4 x^{6} + 4 (12 x^{5}) + 4 (60 x^{4}) + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Simplify.

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Multiply $12$ by $4$ .

$(4 x^{6} + 48 x^{5} + 4 (60 x^{4}) + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $60$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 4 (160 x^{3}) + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $160$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 4 (240 x^{2}) + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $240$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 4 (192 x) + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $192$ by $4$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 4 \cdot 64) {(8 x + 7)}^{3}$

Multiply $4$ by $64$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) {(8 x + 7)}^{3}$

Use the Binomial Theorem.

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) ({(8 x)}^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Simplify each term.

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Apply the product rule to $8 x$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (8^{3} x^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Raise $8$ to the power of $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 {(8 x)}^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Apply the product rule to $8 x$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 (8^{2} x^{2}) \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Raise $8$ to the power of $2$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 3 (64 x^{2}) \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $64$ by $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 192 x^{2} \cdot 7 + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $7$ by $192$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 3 (8 x) \cdot 7^{2} + 7^{3})$

Multiply $8$ by $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 24 x \cdot 7^{2} + 7^{3})$

Raise $7$ to the power of $2$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 24 x \cdot 49 + 7^{3})$

Multiply $49$ by $24$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 1176 x + 7^{3})$

Raise $7$ to the power of $3$ .

$(4 x^{6} + 48 x^{5} + 240 x^{4} + 640 x^{3} + 960 x^{2} + 768 x + 256) (512 x^{3} + 1344 x^{2} + 1176 x + 343)$

Simplify terms.

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Simplify each term.

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Rewrite using the commutative property of multiplication.

Multiply $x^{6}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $3$ and $6$ .

Multiply $4$ by $512$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $2$ and $6$ .

Multiply $4$ by $1344$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{6}$ by $x$ by adding the exponents.

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Move $x$ .

Multiply $x$ by $x^{6}$ .

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Raise $x$ to the power of $1$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $1$ and $6$ .

Multiply $4$ by $1176$ .

Multiply $343$ by $4$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $3$ and $5$ .

Multiply $48$ by $512$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $2$ and $5$ .

Multiply $48$ by $1344$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{5}$ by $x$ by adding the exponents.

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Move $x$ .

Multiply $x$ by $x^{5}$ .

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Raise $x$ to the power of $1$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $1$ and $5$ .

Multiply $48$ by $1176$ .

Multiply $343$ by $48$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{4}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $3$ and $4$ .

Multiply $240$ by $512$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $2$ and $4$ .

Multiply $240$ by $1344$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{4}$ by $x$ by adding the exponents.

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Move $x$ .

Multiply $x$ by $x^{4}$ .

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Raise $x$ to the power of $1$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $1$ and $4$ .

Multiply $240$ by $1176$ .

Multiply $343$ by $240$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{3}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Add $3$ and $3$ .

Multiply $640$ by $512$ .

Rewrite using the commutative property of multiplication.

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 (x^{2} x^{3}) + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 x^{2 + 3} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $3$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 640 \cdot 1344 x^{5} + 640 x^{3} (1176 x) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $640$ by $1344$ .

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{3} x + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 (x \cdot x^{3}) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{3}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 (x^{1} x^{3}) + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{1 + 3} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $3$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 640 \cdot 1176 x^{4} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $640$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 640 x^{3} \cdot 343 + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $640$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 x^{2} (512 x^{3}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{2} x^{3} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 (x^{3} x^{2}) + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{3 + 2} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 960 \cdot 512 x^{5} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 x^{2} (1344 x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{2} x^{2} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 (x^{2} x^{2}) + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{2 + 2} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 960 \cdot 1344 x^{4} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 x^{2} (1176 x) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{2} x + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 (x \cdot x^{2}) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{2}$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 (x^{1} x^{2}) + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{1 + 2} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $1$ and $2$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 960 \cdot 1176 x^{3} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $960$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 960 x^{2} \cdot 343 + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $960$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 x (512 x^{3}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x \cdot x^{3} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{3}$ by adding the exponents.

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Move $x^{3}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 (x^{3} x) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{3}$ by $x$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 (x^{3} x^{1}) + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x^{3 + 1} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $3$ and $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 768 \cdot 512 x^{4} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $512$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 x (1344 x^{2}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x \cdot x^{2} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 (x^{2} x) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x^{2}$ by $x$ .

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Raise $x$ to the power of $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 (x^{2} x^{1}) + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x^{2 + 1} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Add $2$ and $1$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 768 \cdot 1344 x^{3} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $1344$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 x (1176 x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Rewrite using the commutative property of multiplication.

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 x \cdot x + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 (x \cdot x) + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $x$ by $x$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 768 \cdot 1176 x^{2} + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $768$ by $1176$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 768 x \cdot 343 + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $343$ by $768$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 256 (512 x^{3}) + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $512$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 256 (1344 x^{2}) + 256 (1176 x) + 256 \cdot 343$

Multiply $1344$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 256 (1176 x) + 256 \cdot 343$

Multiply $1176$ by $256$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 256 \cdot 343$

Multiply $256$ by $343$ .

$2048 x^{9} + 5376 x^{8} + 4704 x^{7} + 1372 x^{6} + 24576 x^{8} + 64512 x^{7} + 56448 x^{6} + 16464 x^{5} + 122880 x^{7} + 322560 x^{6} + 282240 x^{5} + 82320 x^{4} + 327680 x^{6} + 860160 x^{5} + 752640 x^{4} + 219520 x^{3} + 491520 x^{5} + 1290240 x^{4} + 1128960 x^{3} + 329280 x^{2} + 393216 x^{4} + 1032192 x^{3} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Simplify by adding terms.

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Add $5376 x^{8}$ and $24576 x^{8}$ .

Add $4704 x^{7}$ and $64512 x^{7}$ .

Add $69216 x^{7}$ and $122880 x^{7}$ .

Add $1372 x^{6}$ and $56448 x^{6}$ .

Add $57820 x^{6}$ and $322560 x^{6}$ .

Add $380380 x^{6}$ and $327680 x^{6}$ .

Add $16464 x^{5}$ and $282240 x^{5}$ .

Add $298704 x^{5}$ and $860160 x^{5}$ .

Add $1158864 x^{5}$ and $491520 x^{5}$ .

Add $82320 x^{4}$ and $752640 x^{4}$ .

Add $834960 x^{4}$ and $1290240 x^{4}$ .

Add $2125200 x^{4}$ and $393216 x^{4}$ .

Add $219520 x^{3}$ and $1128960 x^{3}$ .

Add $1348480 x^{3}$ and $1032192 x^{3}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2380672 x^{3} + 329280 x^{2} + 903168 x^{2} + 263424 x + 131072 x^{3} + 344064 x^{2} + 301056 x + 87808$

Add $2380672 x^{3}$ and $131072 x^{3}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 329280 x^{2} + 903168 x^{2} + 263424 x + 344064 x^{2} + 301056 x + 87808$

Add $329280 x^{2}$ and $903168 x^{2}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1232448 x^{2} + 263424 x + 344064 x^{2} + 301056 x + 87808$

Add $1232448 x^{2}$ and $344064 x^{2}$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1576512 x^{2} + 263424 x + 301056 x + 87808$

Add $263424 x$ and $301056 x$ .

$2048 x^{9} + 29952 x^{8} + 192096 x^{7} + 708060 x^{6} + 1650384 x^{5} + 2518416 x^{4} + 2511744 x^{3} + 1576512 x^{2} + 564480 x + 87808$

The leading term in a polynomial is the term with the highest degree.

$2048 x^{9}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$2048$

Since the leading coefficient is positive, the graph rises to the right.

Positive

Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.

1. Even and Positive: Rises to the left and rises to the right.

2. Even and Negative: Falls to the left and falls to the right.

3. Odd and Positive: Falls to the left and rises to the right.

4. Odd and Negative: Rises to the left and falls to the right

Determine the behavior.

Falls to the left and rises to the right