Factor y^2+6y+9

$y^{2} + 6 y + 9$

Step 1

Rewrite $9$ as $3^{2}$ .

$y^{2} + 6 y + 3^{2}$

Step 2

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

$6 y = 2 \cdot y \cdot 3$

Step 3

Rewrite the polynomial.

$y^{2} + 2 \cdot y \cdot 3 + 3^{2}$

Step 4

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

${(y + 3)}^{2}$