Answer
$(5x-2y)(3x-5y)$
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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$15x^{2}-31xy+10y^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad ac=+150y^{2} \quad(150=6\times 25)$
2. $\quad$sum = $-31y\quad$... factors: $-6y$ and $-25y$
3. $\quad$ $15x^{2}-31xy+10y^{2} = (15x^{2}-25xy)+(-6xy+10y^{2} )$
4. $\quad$... $= 5x(3x-5y)+(-2y)(3x-5y) = (5x-2y)(3x-5y)$
Check by FOIL
$F:\quad 15x^{2}$
$O:\quad -25xy$
$I:\quad -6xy$
$L:\quad +10y^{2}$
$(5x-2y)(3x-5y)$ = $15x^{2}-31xy+10y^{2}$
