Algebra Examples

$(2 x^{3} + 3 x^{2} + 10 x) (8 x^{4})$

Step 1

Apply the distributive property.

$2 x^{3} (8 x^{4}) + 3 x^{2} (8 x^{4}) + 10 x (8 x^{4})$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$2 \cdot 8 x^{3} x^{4} + 3 x^{2} (8 x^{4}) + 10 x (8 x^{4})$

Step 2.2

Rewrite using the commutative property of multiplication.

$2 \cdot 8 x^{3} x^{4} + 3 \cdot 8 x^{2} x^{4} + 10 x (8 x^{4})$

Step 2.3

Rewrite using the commutative property of multiplication.

$2 \cdot 8 x^{3} x^{4} + 3 \cdot 8 x^{2} x^{4} + 10 \cdot 8 x \cdot x^{4}$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{4}$ .

$2 \cdot 8 (x^{4} x^{3}) + 3 \cdot 8 x^{2} x^{4} + 10 \cdot 8 x \cdot x^{4}$

Step 3.1.2

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

$2 \cdot 8 x^{4 + 3} + 3 \cdot 8 x^{2} x^{4} + 10 \cdot 8 x \cdot x^{4}$

Step 3.1.3

Add $4$ and $3$ .

$2 \cdot 8 x^{7} + 3 \cdot 8 x^{2} x^{4} + 10 \cdot 8 x \cdot x^{4}$

Step 3.2

Multiply $2$ by $8$ .

$16 x^{7} + 3 \cdot 8 x^{2} x^{4} + 10 \cdot 8 x \cdot x^{4}$

Step 3.3

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

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Step 3.3.1

Move $x^{4}$ .

$16 x^{7} + 3 \cdot 8 (x^{4} x^{2}) + 10 \cdot 8 x \cdot x^{4}$

Step 3.3.2

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

$16 x^{7} + 3 \cdot 8 x^{4 + 2} + 10 \cdot 8 x \cdot x^{4}$

Step 3.3.3

Add $4$ and $2$ .

$16 x^{7} + 3 \cdot 8 x^{6} + 10 \cdot 8 x \cdot x^{4}$

Step 3.4

Multiply $3$ by $8$ .

$16 x^{7} + 24 x^{6} + 10 \cdot 8 x \cdot x^{4}$

Step 3.5

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

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Step 3.5.1

Move $x^{4}$ .

$16 x^{7} + 24 x^{6} + 10 \cdot 8 (x^{4} x)$

Step 3.5.2

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

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Step 3.5.2.1

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

$16 x^{7} + 24 x^{6} + 10 \cdot 8 (x^{4} x^{1})$

Step 3.5.2.2

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

$16 x^{7} + 24 x^{6} + 10 \cdot 8 x^{4 + 1}$

Step 3.5.3

Add $4$ and $1$ .

$16 x^{7} + 24 x^{6} + 10 \cdot 8 x^{5}$

Step 3.6

Multiply $10$ by $8$ .

$16 x^{7} + 24 x^{6} + 80 x^{5}$