Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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