Factor 49b^2+70b+25

$49 b^{2} + 70 b + 25$

Step 1

Rewrite $49 b^{2}$ as ${(7 b)}^{2}$ .

${(7 b)}^{2} + 70 b + 25$

Step 2

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

${(7 b)}^{2} + 70 b + 5^{2}$

Step 3

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

$70 b = 2 \cdot (7 b) \cdot 5$

Step 4

Rewrite the polynomial.

${(7 b)}^{2} + 2 \cdot (7 b) \cdot 5 + 5^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 7 b$ and $b = 5$ .

${(7 b + 5)}^{2}$