Factor 16x^2+48xy+36y^2

$16 x^{2} + 48 x y + 36 y^{2}$

Step 1

Factor $4$ out of $16 x^{2} + 48 x y + 36 y^{2}$ .

Factor $4$ out of $16 x^{2}$ .

$4 (4 x^{2}) + 48 x y + 36 y^{2}$

Factor $4$ out of $48 x y$ .

$4 (4 x^{2}) + 4 (12 x y) + 36 y^{2}$

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

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

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

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

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

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

Step 2

Factor using the perfect square rule.

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

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

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

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

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

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

Rewrite the polynomial.

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

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

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