Factor 9m^2+30mn+25n^2

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

${(3 m + 5 n)}^{2}$