Answer
$(2a+5b)(a+b)$
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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$2a^{2}+7ab+5b^{2} =...$
Always start by searching for a GCF ... (there are none other than 1).
1. $\quad$"$ac$"$=+10b^{2} $
2. $\quad$sum = $+7b\quad$... factors: $2b$ and $5b$
3. $\quad$ $2a^{2}+7ab+5b^{2} = (2a^{2}++2ab)+( 5ab+5b^{2})$
4. $\quad$... $= 2a(a+b)+5b(a+b) = (2a+5b)(a+b)$
Check by FOIL
$F:\quad 2a^{2}$
$O:\quad +2ab$
$I:\quad +5ab$
$L:\quad +5b^{2}$
$(2a+5b)(a+b)$ = $2a^{2}+7ab+5b^{2}$
