Factor 2x^2y+12xy+18y

$2 x^{2} y + 12 x y + 18 y$

Step 1

Factor $2 y$ out of $2 x^{2} y + 12 x y + 18 y$ .

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

$2 y (x^{2}) + 12 x y + 18 y$

Factor $2 y$ out of $12 x y$ .

$2 y (x^{2}) + 2 y (6 x) + 18 y$

Factor $2 y$ out of $18 y$ .

$2 y (x^{2}) + 2 y (6 x) + 2 y (9)$

Factor $2 y$ out of $2 y (x^{2}) + 2 y (6 x)$ .

$2 y (x^{2} + 6 x) + 2 y (9)$

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

$2 y (x^{2} + 6 x + 9)$

Step 2

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$2 y (x^{2} + 6 x + 3^{2})$

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

$6 x = 2 \cdot x \cdot 3$

Rewrite the polynomial.

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

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

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