Factor 8x^2-24xy+18y^2

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

Step 1

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

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

$2 (4 x^{2}) - 24 x y + 18 y^{2}$

Factor $2$ out of $- 24 x y$ .

$2 (4 x^{2}) + 2 (- 12 x y) + 18 y^{2}$

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

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

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

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

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

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

Step 2

Factor using the perfect square rule.

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

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

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

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

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.

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

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

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