Factor 16y^2+72y+81

$16 y^{2} + 72 y + 81$

Step 1

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

${(4 y)}^{2} + 72 y + 81$

Step 2

Rewrite $81$ as $9^{2}$ .

${(4 y)}^{2} + 72 y + 9^{2}$

Step 3

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

$72 y = 2 \cdot (4 y) \cdot 9$

Step 4

Rewrite the polynomial.

${(4 y)}^{2} + 2 \cdot (4 y) \cdot 9 + 9^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 4 y$ and $b = 9$ .

${(4 y + 9)}^{2}$