Factor 2d^2+16d+32

$2 d^{2} + 16 d + 32$

Step 1

Factor $2$ out of $2 d^{2} + 16 d + 32$ .

Factor $2$ out of $2 d^{2}$ .

$2 (d^{2}) + 16 d + 32$

Factor $2$ out of $16 d$ .

$2 (d^{2}) + 2 (8 d) + 32$

Factor $2$ out of $32$ .

$2 d^{2} + 2 (8 d) + 2 \cdot 16$

Factor $2$ out of $2 d^{2} + 2 (8 d)$ .

$2 (d^{2} + 8 d) + 2 \cdot 16$

Factor $2$ out of $2 (d^{2} + 8 d) + 2 \cdot 16$ .

$2 (d^{2} + 8 d + 16)$

Step 2

Factor using the perfect square rule.

Rewrite $16$ as $4^{2}$ .

$2 (d^{2} + 8 d + 4^{2})$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$8 d = 2 \cdot d \cdot 4$

Rewrite the polynomial.

$2 (d^{2} + 2 \cdot d \cdot 4 + 4^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = d$ and $b = 4$ .

$2 {(d + 4)}^{2}$