Factor 4x^2-12xy+9y^2

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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