Factor 81y^2+126y+49

$81 y^{2} + 126 y + 49$

Step 1

Rewrite $81 y^{2}$ as ${(9 y)}^{2}$ .

${(9 y)}^{2} + 126 y + 49$

Step 2

Rewrite $49$ as $7^{2}$ .

${(9 y)}^{2} + 126 y + 7^{2}$

Step 3

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

$126 y = 2 \cdot (9 y) \cdot 7$

Step 4

Rewrite the polynomial.

${(9 y)}^{2} + 2 \cdot (9 y) \cdot 7 + 7^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 9 y$ and $b = 7$ .

${(9 y + 7)}^{2}$