Factor 4z^2+12z+9

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

Step 1

Rewrite $4 z^{2}$ as ${(2 z)}^{2}$ .

${(2 z)}^{2} + 12 z + 9$

Step 2

Rewrite $9$ as $3^{2}$ .

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

Step 3

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

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

Step 4

Rewrite the polynomial.

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

Step 5

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

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