Simplify: a^2 b^2(a+2 b)(3 a+b) - Vidyadip

Question

Simplify:
$a^2 b^2(a+2 b)(3 a+b)$

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Answer

To simplify, we will proceed as follows: $a^2 b^2(a+2 b)(3 a+b)$
$=\left[a^2 b^2(a+2 b)\right](3 a+b)$
$=\left(a^3 b^2+2 a^2 b^3(3 a+b)\right.$
$=3 a\left(a^3 b^2+2 a^2 b^3\right)+b\left(a^3 b^2+2 a^2 b^3\right)$
$=3 a^4 b^2+6 a^3 b^3+a^3 b^3+2 a^2 b^4 .$
$=3 a^4 b^2+7 a^3 b^3+2 a^2 b^4$
Thus, the answer is $3 a^4 b^2+7 a^3 b^3+2 a^2 b^4$

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