Factor 25w^2-60w+36

$25 w^{2} - 60 w + 36$

Step 1

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

${(5 w)}^{2} - 60 w + 36$

Step 2

Rewrite $36$ as $6^{2}$ .

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

Step 3

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

$60 w = 2 \cdot (5 w) \cdot 6$

Step 4

Rewrite the polynomial.

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

Step 5

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

${(5 w - 6)}^{2}$