Factor 9m^2-30m+25

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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