Factor 36x^2-60xy+25y^2

$36 x^{2} - 60 x y + 25 y^{2}$

Step 1

Rewrite $36 x^{2}$ as ${(6 x)}^{2}$ .

${(6 x)}^{2} - 60 x y + 25 y^{2}$

Step 2

Rewrite $25 y^{2}$ as ${(5 y)}^{2}$ .

${(6 x)}^{2} - 60 x y + {(5 y)}^{2}$

Step 3

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

$60 x y = 2 \cdot (6 x) \cdot (5 y)$

Step 4

Rewrite the polynomial.

${(6 x)}^{2} - 2 \cdot (6 x) \cdot (5 y) + {(5 y)}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 6 x$ and $b = 5 y$ .

${(6 x - 5 y)}^{2}$