Factor 4a^2-12ab+9b^2

$4 a^{2} - 12 a b + 9 b^{2}$

Step 1

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

${(2 a)}^{2} - 12 a b + 9 b^{2}$

Step 2

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

${(2 a)}^{2} - 12 a b + {(3 b)}^{2}$

Step 3

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

$12 a b = 2 \cdot (2 a) \cdot (3 b)$

Step 4

Rewrite the polynomial.

${(2 a)}^{2} - 2 \cdot (2 a) \cdot (3 b) + {(3 b)}^{2}$

Step 5

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

${(2 a - 3 b)}^{2}$