Answer
$ (3z+2)(3z+2) $
Work Step by Step
Factoring by grouping:
1. Multiply the leading coefficient, a, and the constant, c.
2. Find the factors of ac whose sum is b.
3. Rewrite the middle term, bx, as a sum or difference using the factors from step 2.
4. Factor by grouping
---
$9z^{2}+12z+4 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=36\qquad $
2. $\quad$sum = $+12 \quad$... factors: $+6$ and $+6$
3. $\quad 9z^{2}+12z+4 =(9z^{2}+6z)+(6z+4)$
4. $\quad$... $=3z(3z+2) +(2)(3z+2) = (3z+2)(3z+2)$
Check by FOIL
$F:\quad 9z^{2}$
$O:\quad +6z$
$I:\quad +6z$
$L:\quad +4$
$ (3z+2)(3z+2) $ = $9z^{2}+12z+4$
