Answer
$ (3a-7b)(a+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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$3a^{2}-ab-14b^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad$"$ac$"$=-42b^{2} $
2. $\quad$sum = $-b\quad$... factors: $-7b$ and $+6b$
3. $\quad$ $3a^{2}-ab-14b^{2} = (3a^{2}+6ab)+( -7ab-14b^{2})$
4. $\quad$... $= 3a(a+2b)+(-7b)(a+2b) = (3a-7b)(a+2b) $
Check by FOIL
$F:\quad 3a^{2}$
$O:\quad +6ab$
$I:\quad -7ab$
$L:\quad -14b^{2}$
$ (3a-7b)(a+2b) $ = $3a^{2}-ab-14b^{2} $
