Simplify (a+6)(a^2-8a+8)

$(a + 6) (a^{2} - 8 a + 8)$

Step 1

Expand $(a + 6) (a^{2} - 8 a + 8)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (- 8 a) + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$a^{1} a^{2} + a (- 8 a) + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

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

$a^{1 + 2} + a (- 8 a) + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

Add $1$ and $2$ .

$a^{3} + a (- 8 a) + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

Rewrite using the commutative property of multiplication.

$a^{3} - 8 a \cdot a + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

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

Move $a$ .

$a^{3} - 8 (a \cdot a) + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

Multiply $a$ by $a$ .

$a^{3} - 8 a^{2} + a \cdot 8 + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

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

$a^{3} - 8 a^{2} + 8 \cdot a + 6 a^{2} + 6 (- 8 a) + 6 \cdot 8$

Multiply $- 8$ by $6$ .

$a^{3} - 8 a^{2} + 8 a + 6 a^{2} - 48 a + 6 \cdot 8$

Multiply $6$ by $8$ .

$a^{3} - 8 a^{2} + 8 a + 6 a^{2} - 48 a + 48$

Simplify by adding terms.

Add $- 8 a^{2}$ and $6 a^{2}$ .

$a^{3} - 2 a^{2} + 8 a - 48 a + 48$

Subtract $48 a$ from $8 a$ .

$a^{3} - 2 a^{2} - 40 a + 48$