Answer
$ (5z-3)(5z-3) $
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
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$25z^{2}-30z+9 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=225\qquad (25\times 9=5\times 5\times 3\times 3)$
2. $\quad$sum = $-30 \quad$... factors: $-15$ and $-15$
3. $\quad 25z^{2}-30z+9 =(25z^{2}-15z)+(-15z+9)$
4. $\quad$... $=5z(5z-3) +(-3)(5z-3) = (5z-3)(5z-3)$
Check by FOIL
$F:\quad 25z^{2}$
$O:\quad -15z$
$I:\quad -15z$
$L:\quad +9$
$ (5z-3)(5z-3) $ = $25z^{2}-30z+9$
