Basic Math Examples

${(z + 13)}^{6} (z^{2} + 26 z + 175)$

Step 1

Use the Binomial Theorem.

$(z^{6} + 6 z^{5} \cdot 13 + 15 z^{4} \cdot 13^{2} + 20 z^{3} \cdot 13^{3} + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2

Simplify each term.

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Step 2.1

Multiply $13$ by $6$ .

$(z^{6} + 78 z^{5} + 15 z^{4} \cdot 13^{2} + 20 z^{3} \cdot 13^{3} + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.2

Raise $13$ to the power of $2$ .

$(z^{6} + 78 z^{5} + 15 z^{4} \cdot 169 + 20 z^{3} \cdot 13^{3} + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.3

Multiply $169$ by $15$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 20 z^{3} \cdot 13^{3} + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.4

Raise $13$ to the power of $3$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 20 z^{3} \cdot 2197 + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.5

Multiply $2197$ by $20$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 15 z^{2} \cdot 13^{4} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.6

Raise $13$ to the power of $4$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 15 z^{2} \cdot 28561 + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.7

Multiply $28561$ by $15$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 428415 z^{2} + 6 z \cdot 13^{5} + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.8

Raise $13$ to the power of $5$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 428415 z^{2} + 6 z \cdot 371293 + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.9

Multiply $371293$ by $6$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 428415 z^{2} + 2227758 z + 13^{6}) (z^{2} + 26 z + 175)$

Step 2.10

Raise $13$ to the power of $6$ .

$(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 428415 z^{2} + 2227758 z + 4826809) (z^{2} + 26 z + 175)$

Step 3

Expand $(z^{6} + 78 z^{5} + 2535 z^{4} + 43940 z^{3} + 428415 z^{2} + 2227758 z + 4826809) (z^{2} + 26 z + 175)$ by multiplying each term in the first expression by each term in the second expression.

$z^{6} z^{2} + z^{6} (26 z) + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

$z^{6 + 2} + z^{6} (26 z) + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.1.2

Add $6$ and $2$ .

$z^{8} + z^{6} (26 z) + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.2

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{6} z + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.3

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

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Step 4.1.3.1

Move $z$ .

$z^{8} + 26 (z \cdot z^{6}) + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.3.2

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

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Step 4.1.3.2.1

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

$z^{8} + 26 (z^{1} z^{6}) + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.3.2.2

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

$z^{8} + 26 z^{1 + 6} + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.3.3

Add $1$ and $6$ .

$z^{8} + 26 z^{7} + z^{6} \cdot 175 + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.4

Move $175$ to the left of $z^{6}$ .

$z^{8} + 26 z^{7} + 175 \cdot z^{6} + 78 z^{5} z^{2} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.5

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

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Step 4.1.5.1

Move $z^{2}$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 (z^{2} z^{5}) + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.5.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{2 + 5} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.5.3

Add $2$ and $5$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 z^{5} (26 z) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.6

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 \cdot 26 z^{5} z + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.7

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

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Step 4.1.7.1

Move $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 \cdot 26 (z \cdot z^{5}) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.7.2

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

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Step 4.1.7.2.1

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 \cdot 26 (z^{1} z^{5}) + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.7.2.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 \cdot 26 z^{1 + 5} + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.7.3

Add $1$ and $5$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 78 \cdot 26 z^{6} + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.8

Multiply $78$ by $26$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 78 z^{5} \cdot 175 + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.9

Multiply $175$ by $78$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{4} z^{2} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.10

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

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Step 4.1.10.1

Move $z^{2}$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 (z^{2} z^{4}) + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.10.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{2 + 4} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.10.3

Add $2$ and $4$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 z^{4} (26 z) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.11

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 \cdot 26 z^{4} z + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.12

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

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Step 4.1.12.1

Move $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 \cdot 26 (z \cdot z^{4}) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.12.2

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

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Step 4.1.12.2.1

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 \cdot 26 (z^{1} z^{4}) + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.12.2.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 \cdot 26 z^{1 + 4} + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.12.3

Add $1$ and $4$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 2535 \cdot 26 z^{5} + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.13

Multiply $2535$ by $26$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 2535 z^{4} \cdot 175 + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.14

Multiply $175$ by $2535$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{3} z^{2} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.15

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

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Step 4.1.15.1

Move $z^{2}$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 (z^{2} z^{3}) + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.15.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{2 + 3} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.15.3

Add $2$ and $3$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 z^{3} (26 z) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.16

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 \cdot 26 z^{3} z + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.17

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

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Step 4.1.17.1

Move $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 \cdot 26 (z \cdot z^{3}) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.17.2

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

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Step 4.1.17.2.1

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 \cdot 26 (z^{1} z^{3}) + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.17.2.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 \cdot 26 z^{1 + 3} + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.17.3

Add $1$ and $3$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 43940 \cdot 26 z^{4} + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.18

Multiply $43940$ by $26$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 43940 z^{3} \cdot 175 + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.19

Multiply $175$ by $43940$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{2} z^{2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.20

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

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Step 4.1.20.1

Move $z^{2}$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 (z^{2} z^{2}) + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.20.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{2 + 2} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.20.3

Add $2$ and $2$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 z^{2} (26 z) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.21

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 \cdot 26 z^{2} z + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.22

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

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Step 4.1.22.1

Move $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 \cdot 26 (z \cdot z^{2}) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.22.2

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

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Step 4.1.22.2.1

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 \cdot 26 (z^{1} z^{2}) + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.22.2.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 \cdot 26 z^{1 + 2} + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.22.3

Add $1$ and $2$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 428415 \cdot 26 z^{3} + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.23

Multiply $428415$ by $26$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 428415 z^{2} \cdot 175 + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.24

Multiply $175$ by $428415$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z \cdot z^{2} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.25

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

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Step 4.1.25.1

Move $z^{2}$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 (z^{2} z) + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.25.2

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

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Step 4.1.25.2.1

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 (z^{2} z^{1}) + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.25.2.2

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

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{2 + 1} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.25.3

Add $2$ and $1$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 2227758 z (26 z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.26

Rewrite using the commutative property of multiplication.

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 2227758 \cdot 26 z \cdot z + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.27

Multiply $z$ by $z$ by adding the exponents.

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Step 4.1.27.1

Move $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 2227758 \cdot 26 (z \cdot z) + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.27.2

Multiply $z$ by $z$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 2227758 \cdot 26 z^{2} + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.28

Multiply $2227758$ by $26$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 2227758 z \cdot 175 + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.29

Multiply $175$ by $2227758$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 4826809 (26 z) + 4826809 \cdot 175$

Step 4.1.30

Multiply $26$ by $4826809$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 4826809 \cdot 175$

Step 4.1.31

Multiply $4826809$ by $175$ .

$z^{8} + 26 z^{7} + 175 z^{6} + 78 z^{7} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Add $26 z^{7}$ and $78 z^{7}$ .

$z^{8} + 104 z^{7} + 175 z^{6} + 2028 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.2

Add $175 z^{6}$ and $2028 z^{6}$ .

$z^{8} + 104 z^{7} + 2203 z^{6} + 13650 z^{5} + 2535 z^{6} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.3

Add $2203 z^{6}$ and $2535 z^{6}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 13650 z^{5} + 65910 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.4

Add $13650 z^{5}$ and $65910 z^{5}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 79560 z^{5} + 443625 z^{4} + 43940 z^{5} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.5

Add $79560 z^{5}$ and $43940 z^{5}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 443625 z^{4} + 1142440 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.6

Add $443625 z^{4}$ and $1142440 z^{4}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 1586065 z^{4} + 7689500 z^{3} + 428415 z^{4} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.7

Add $1586065 z^{4}$ and $428415 z^{4}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 7689500 z^{3} + 11138790 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.8

Add $7689500 z^{3}$ and $11138790 z^{3}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 18828290 z^{3} + 74972625 z^{2} + 2227758 z^{3} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.9

Add $18828290 z^{3}$ and $2227758 z^{3}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 21056048 z^{3} + 74972625 z^{2} + 57921708 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.10

Add $74972625 z^{2}$ and $57921708 z^{2}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 21056048 z^{3} + 132894333 z^{2} + 389857650 z + 4826809 z^{2} + 125497034 z + 844691575$

Step 4.2.11

Add $132894333 z^{2}$ and $4826809 z^{2}$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 21056048 z^{3} + 137721142 z^{2} + 389857650 z + 125497034 z + 844691575$

Step 4.2.12

Add $389857650 z$ and $125497034 z$ .

$z^{8} + 104 z^{7} + 4738 z^{6} + 123500 z^{5} + 2014480 z^{4} + 21056048 z^{3} + 137721142 z^{2} + 515354684 z + 844691575$