Factor 9b^2-30a^2b+25a^4

$9 b^{2} - 30 a^{2} b + 25 a^{4}$

Step 1

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

${(3 b)}^{2} - 30 a^{2} b + 25 a^{4}$

Step 2

Rewrite $25 a^{4}$ as ${(5 a^{2})}^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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