Algebra Examples

$(8 + w) (64 - 8 w + w^{2})$

Step 1

Expand $(8 + w) (64 - 8 w + w^{2})$ by multiplying each term in the first expression by each term in the second expression.

$8 \cdot 64 + 8 (- 8 w) + 8 w^{2} + w \cdot 64 + w (- 8 w) + w \cdot w^{2}$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $8$ by $64$ .

$512 + 8 (- 8 w) + 8 w^{2} + w \cdot 64 + w (- 8 w) + w \cdot w^{2}$

Step 2.1.2

Multiply $- 8$ by $8$ .

$512 - 64 w + 8 w^{2} + w \cdot 64 + w (- 8 w) + w \cdot w^{2}$

Step 2.1.3

Move $64$ to the left of $w$ .

$512 - 64 w + 8 w^{2} + 64 \cdot w + w (- 8 w) + w \cdot w^{2}$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$512 - 64 w + 8 w^{2} + 64 w - 8 w \cdot w + w \cdot w^{2}$

Step 2.1.5

Multiply $w$ by $w$ by adding the exponents.

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Step 2.1.5.1

Move $w$ .

$512 - 64 w + 8 w^{2} + 64 w - 8 (w \cdot w) + w \cdot w^{2}$

Step 2.1.5.2

Multiply $w$ by $w$ .

$512 - 64 w + 8 w^{2} + 64 w - 8 w^{2} + w \cdot w^{2}$

Step 2.1.6

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

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Step 2.1.6.1

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

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Step 2.1.6.1.1

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

$512 - 64 w + 8 w^{2} + 64 w - 8 w^{2} + w^{1} w^{2}$

Step 2.1.6.1.2

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

$512 - 64 w + 8 w^{2} + 64 w - 8 w^{2} + w^{1 + 2}$

Step 2.1.6.2

Add $1$ and $2$ .

$512 - 64 w + 8 w^{2} + 64 w - 8 w^{2} + w^{3}$

Step 2.2

Combine the opposite terms in $512 - 64 w + 8 w^{2} + 64 w - 8 w^{2} + w^{3}$ .

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Step 2.2.1

Add $- 64 w$ and $64 w$ .

$512 + 8 w^{2} + 0 - 8 w^{2} + w^{3}$

Step 2.2.2

Add $512 + 8 w^{2}$ and $0$ .

$512 + 8 w^{2} - 8 w^{2} + w^{3}$

Step 2.2.3

Subtract $8 w^{2}$ from $8 w^{2}$ .

$512 + 0 + w^{3}$

Step 2.2.4

Add $512$ and $0$ .

$512 + w^{3}$