Question

Solve:
$[\frac{3}{4}{a}^2+3b^2]\times \left[4\right(a^2-\frac{2}{3}{b}^2\left)\right]$

Answer 1

We have,

$=[\frac{3}{4}{a}^2+3b^2]\times \left[4(a^2-\frac{2}{3}{b}^2)\right]$

$=[\frac{3}{4}{a}^2+3b^2]\times [4a^2-\frac{8}{3}{b}^2]$

$=\frac{12}{4}{a}^4-\frac{24}{12}{a}^2{b}^2+12a^2{b}^2-\frac{24}{3}{b}^4$

$=3a^4-2a^2{b}^2+12a^2{b}^2-8b^4$

$=3a^4+10a^2{b}^2-8b^4$

Hence, this is the answer.