Answer
$(3y-2)(3y-1)$
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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$9y^{2}-9y+2 =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+18$
2. $\quad$sum = $-9\quad$... factors: $-6$ and $-3$
3. $\quad$ $9y^{2}-9y+2 = ( 9y^{2}-6y)+(-3y+2)$
4. $\quad$... $= 3y(3y-2)+(-1)(3y-2) = (3y-2)(3y-1)$
Check by FOIL
$F:\quad 9y^{2}$
$O:\quad -3y$
$I:\quad -6y$
$L:\quad +2$
$(3y-2)(3y-1)$ = $9y^{2}-9y+2$
