Factor 9c^2+24c+16

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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