Question
Expand$: \left(3 a+\frac{2}{b}\right)\left(2 a-\frac{3}{b}\right)$
✓
Answer
$ \left(3 a+\frac{2}{b}\right)\left(2 a-\frac{3}{b}\right)$
$=(3 a)(2 a)+\left(\frac{2}{b}\right)(2 a)-\left(\frac{3}{b}\right)(3 a)-\left(\frac{2}{b}\right)\left(\frac{3}{b}\right)$
$ =6 a^2+\left(\frac{4}{b}-\frac{9}{b}\right) a-\frac{6}{b^2}$
$ =6 a^2+\left(-\frac{5}{b}\right) a-\frac{6}{b^2}$
$ =6 a^2-\frac{5 a}{b}-\frac{6}{b^2}$
$=(3 a)(2 a)+\left(\frac{2}{b}\right)(2 a)-\left(\frac{3}{b}\right)(3 a)-\left(\frac{2}{b}\right)\left(\frac{3}{b}\right)$
$ =6 a^2+\left(\frac{4}{b}-\frac{9}{b}\right) a-\frac{6}{b^2}$
$ =6 a^2+\left(-\frac{5}{b}\right) a-\frac{6}{b^2}$
$ =6 a^2-\frac{5 a}{b}-\frac{6}{b^2}$
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