Factor 25a^2+9b^2+30ab

$25 a^{2} + 9 b^{2} + 30 a b$

Step 1

Rearrange terms.

$25 a^{2} + 30 a b + 9 b^{2}$

Step 2

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

${(5 a)}^{2} + 30 a b + 9 b^{2}$

Step 3

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

${(5 a)}^{2} + 30 a b + {(3 b)}^{2}$

Step 4

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

$30 a b = 2 \cdot (5 a) \cdot (3 b)$

Step 5

Rewrite the polynomial.

${(5 a)}^{2} + 2 \cdot (5 a) \cdot (3 b) + {(3 b)}^{2}$

Step 6

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

${(5 a + 3 b)}^{2}$