Simplify (a+4)(a^2-6a+6)

$(a + 4) (a^{2} - 6 a + 6)$

Step 1

Expand $(a + 4) (a^{2} - 6 a + 6)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (- 6 a) + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

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 $1$ .

$a^{1} a^{2} + a (- 6 a) + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

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

$a^{1 + 2} + a (- 6 a) + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

Add $1$ and $2$ .

$a^{3} + a (- 6 a) + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

Rewrite using the commutative property of multiplication.

$a^{3} - 6 a \cdot a + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

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

Move $a$ .

$a^{3} - 6 (a \cdot a) + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

Multiply $a$ by $a$ .

$a^{3} - 6 a^{2} + a \cdot 6 + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

Move $6$ to the left of $a$ .

$a^{3} - 6 a^{2} + 6 \cdot a + 4 a^{2} + 4 (- 6 a) + 4 \cdot 6$

Multiply $- 6$ by $4$ .

$a^{3} - 6 a^{2} + 6 a + 4 a^{2} - 24 a + 4 \cdot 6$

Multiply $4$ by $6$ .

$a^{3} - 6 a^{2} + 6 a + 4 a^{2} - 24 a + 24$

Simplify by adding terms.

Add $- 6 a^{2}$ and $4 a^{2}$ .

$a^{3} - 2 a^{2} + 6 a - 24 a + 24$

Subtract $24 a$ from $6 a$ .

$a^{3} - 2 a^{2} - 18 a + 24$