Factor 2x^2+8x+8

$2 x^{2} + 8 x + 8$

Step 1

Factor $2$ out of $2 x^{2} + 8 x + 8$ .

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

$2 (x^{2}) + 8 x + 8$

Factor $2$ out of $8 x$ .

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

Factor $2$ out of $8$ .

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

Factor $2$ out of $2 x^{2} + 2 (4 x)$ .

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

Factor $2$ out of $2 (x^{2} + 4 x) + 2 \cdot 4$ .

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

Step 2

Factor using the perfect square rule.

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

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

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

$4 x = 2 \cdot x \cdot 2$

Rewrite the polynomial.

$2 (x^{2} + 2 \cdot x \cdot 2 + 2^{2})$

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

$2 {(x + 2)}^{2}$