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