Factor w^2+12w+36

$w^{2} + 12 w + 36$

Step 1

Rewrite $36$ as $6^{2}$ .

$w^{2} + 12 w + 6^{2}$

Step 2

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

$12 w = 2 \cdot w \cdot 6$

Step 3

Rewrite the polynomial.

$w^{2} + 2 \cdot w \cdot 6 + 6^{2}$

Step 4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = w$ and $b = 6$ .

${(w + 6)}^{2}$