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