Factor 9v^2+24v+16

$9 v^{2} + 24 v + 16$

Step 1

Rewrite $9 v^{2}$ as ${(3 v)}^{2}$ .

${(3 v)}^{2} + 24 v + 16$

Step 2

Rewrite $16$ as $4^{2}$ .

${(3 v)}^{2} + 24 v + 4^{2}$

Step 3

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

$24 v = 2 \cdot (3 v) \cdot 4$

Step 4

Rewrite the polynomial.

${(3 v)}^{2} + 2 \cdot (3 v) \cdot 4 + 4^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 3 v$ and $b = 4$ .

${(3 v + 4)}^{2}$