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