Simplify (a+2)(a^2-8a+8)

$(a + 2) (a^{2} - 8 a + 8)$

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

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

Simplify terms.

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Simplify each term.

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

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

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

$a^{1} a^{2} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

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

$a^{1 + 2} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Add $1$ and $2$ .

$a^{3} + a (- 8 a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Rewrite using the commutative property of multiplication.

$a^{3} - 8 a \cdot a + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Multiply $a$ by $a$ by adding the exponents.

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Move $a$ .

$a^{3} - 8 (a \cdot a) + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Multiply $a$ by $a$ .

$a^{3} - 8 a^{2} + a \cdot 8 + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Move $8$ to the left of $a$ .

$a^{3} - 8 a^{2} + 8 \cdot a + 2 a^{2} + 2 (- 8 a) + 2 \cdot 8$

Multiply $- 8$ by $2$ .

$a^{3} - 8 a^{2} + 8 a + 2 a^{2} - 16 a + 2 \cdot 8$

Multiply $2$ by $8$ .

$a^{3} - 8 a^{2} + 8 a + 2 a^{2} - 16 a + 16$

Simplify by adding terms.

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Add $- 8 a^{2}$ and $2 a^{2}$ .

$a^{3} - 6 a^{2} + 8 a - 16 a + 16$

Subtract $16 a$ from $8 a$ .

$a^{3} - 6 a^{2} - 8 a + 16$

Simplify (a+2)(a^2-8a+8)

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