Answer
$(5a+3b)(3a-2b)$
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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$15a^{2}-ab-6b^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad$"$ac$"$=-90b^{2} $
2. $\quad$sum = $-b\quad$... factors: $-10b$ and $+9b$
3. $\quad$ $15a^{2}-ab-6b^{2} = (15a^{2}-10ab)+( 9ab-6b^{2})$
4. $\quad$... $= 5a(3a-2b)+3b(3a-2b) = (5a+3b)(3a-2b) $
Check by FOIL
$F:\quad 15a^{2}$
$O:\quad -10ab$
$I:\quad +9ab$
$L:\quad -6b^{2}$
$(5a+3b)(3a-2b)$ = $15a^{2}-ab-6b^{2}$
