Factor v^2+12v+36

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

Step 1

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

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

Step 2

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

$12 v = 2 \cdot v \cdot 6$

Step 3

Rewrite the polynomial.

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

Step 4

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

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