Simplify (a-4)(a^2+4a+16)

$(a - 4) (a^{2} + 4 a + 16)$

Step 1

Expand $(a - 4) (a^{2} + 4 a + 16)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (4 a) + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

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 $1$ .

$a^{1} a^{2} + a (4 a) + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

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

$a^{1 + 2} + a (4 a) + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

Add $1$ and $2$ .

$a^{3} + a (4 a) + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

Rewrite using the commutative property of multiplication.

$a^{3} + 4 a \cdot a + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

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

Move $a$ .

$a^{3} + 4 (a \cdot a) + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

Multiply $a$ by $a$ .

$a^{3} + 4 a^{2} + a \cdot 16 - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

Move $16$ to the left of $a$ .

$a^{3} + 4 a^{2} + 16 \cdot a - 4 a^{2} - 4 (4 a) - 4 \cdot 16$

Multiply $4$ by $- 4$ .

$a^{3} + 4 a^{2} + 16 a - 4 a^{2} - 16 a - 4 \cdot 16$

Multiply $- 4$ by $16$ .

$a^{3} + 4 a^{2} + 16 a - 4 a^{2} - 16 a - 64$

Combine the opposite terms in $a^{3} + 4 a^{2} + 16 a - 4 a^{2} - 16 a - 64$ .

Subtract $4 a^{2}$ from $4 a^{2}$ .

$a^{3} + 16 a + 0 - 16 a - 64$

Add $a^{3} + 16 a$ and $0$ .

$a^{3} + 16 a - 16 a - 64$

Subtract $16 a$ from $16 a$ .

$a^{3} + 0 - 64$

Add $a^{3}$ and $0$ .

$a^{3} - 64$