Factor 9a^2+12a+4

$9 a^{2} + 12 a + 4$

Step 1

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

${(3 a)}^{2} + 12 a + 4$

Step 2

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

${(3 a)}^{2} + 12 a + 2^{2}$

Step 3

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

$12 a = 2 \cdot (3 a) \cdot 2$

Step 4

Rewrite the polynomial.

${(3 a)}^{2} + 2 \cdot (3 a) \cdot 2 + 2^{2}$

Step 5

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

${(3 a + 2)}^{2}$