Factor 9y^2-30y+25

$9 y^{2} - 30 y + 25$

Step 1

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

${(3 y)}^{2} - 30 y + 25$

Step 2

Rewrite $25$ as $5^{2}$ .

${(3 y)}^{2} - 30 y + 5^{2}$

Step 3

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

$30 y = 2 \cdot (3 y) \cdot 5$

Step 4

Rewrite the polynomial.

${(3 y)}^{2} - 2 \cdot (3 y) \cdot 5 + 5^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 y$ and $b = 5$ .

${(3 y - 5)}^{2}$