Factor 9x^2-48xy+64y^2

$9 x^{2} - 48 x y + 64 y^{2}$

Step 1

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

${(3 x)}^{2} - 48 x y + 64 y^{2}$

Step 2

Rewrite $64 y^{2}$ as ${(8 y)}^{2}$ .

${(3 x)}^{2} - 48 x y + {(8 y)}^{2}$

Step 3

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

$48 x y = 2 \cdot (3 x) \cdot (8 y)$

Step 4

Rewrite the polynomial.

${(3 x)}^{2} - 2 \cdot (3 x) \cdot (8 y) + {(8 y)}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 x$ and $b = 8 y$ .

${(3 x - 8 y)}^{2}$