Factor v^2+14v+49

$v^{2} + 14 v + 49$

Step 1

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

$v^{2} + 14 v + 7^{2}$

Step 2

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

$14 v = 2 \cdot v \cdot 7$

Step 3

Rewrite the polynomial.

$v^{2} + 2 \cdot v \cdot 7 + 7^{2}$

Step 4

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

${(v + 7)}^{2}$