Factor 18x^2+24x+8

$18 x^{2} + 24 x + 8$

Step 1

Factor $2$ out of $18 x^{2} + 24 x + 8$ .

Factor $2$ out of $18 x^{2}$ .

$2 (9 x^{2}) + 24 x + 8$

Factor $2$ out of $24 x$ .

$2 (9 x^{2}) + 2 (12 x) + 8$

Factor $2$ out of $8$ .

$2 (9 x^{2}) + 2 (12 x) + 2 (4)$

Factor $2$ out of $2 (9 x^{2}) + 2 (12 x)$ .

$2 (9 x^{2} + 12 x) + 2 (4)$

Factor $2$ out of $2 (9 x^{2} + 12 x) + 2 (4)$ .

$2 (9 x^{2} + 12 x + 4)$

Step 2

Factor using the perfect square rule.

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

$2 ({(3 x)}^{2} + 12 x + 4)$

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

$2 ({(3 x)}^{2} + 12 x + 2^{2})$

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

$12 x = 2 \cdot (3 x) \cdot 2$

Rewrite the polynomial.

$2 ({(3 x)}^{2} + 2 \cdot (3 x) \cdot 2 + 2^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3 x$ and $b = 2$ .

$2 {(3 x + 2)}^{2}$