Factor 4+24x+36x^2

$4 + 24 x + 36 x^{2}$

Step 1

Factor $4$ out of $4 + 24 x + 36 x^{2}$ .

Factor $4$ out of $4$ .

$4 (1) + 24 x + 36 x^{2}$

Factor $4$ out of $24 x$ .

$4 (1) + 4 (6 x) + 36 x^{2}$

Factor $4$ out of $36 x^{2}$ .

$4 (1) + 4 (6 x) + 4 (9 x^{2})$

Factor $4$ out of $4 (1) + 4 (6 x)$ .

$4 (1 + 6 x) + 4 (9 x^{2})$

Factor $4$ out of $4 (1 + 6 x) + 4 (9 x^{2})$ .

$4 (1 + 6 x + 9 x^{2})$

Step 2

Factor using the perfect square rule.

Rewrite $1$ as $1^{2}$ .

$4 (1^{2} + 6 x + 9 x^{2})$

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

$4 (1^{2} + 6 x + {(3 x)}^{2})$

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

$6 x = 2 \cdot 1 \cdot (3 x)$

Rewrite the polynomial.

$4 (1^{2} + 2 \cdot 1 \cdot (3 x) + {(3 x)}^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 1$ and $b = 3 x$ .

$4 {(1 + 3 x)}^{2}$