Question

Multiply the binomials.
$\left(\frac{3}{4}{a}^2+3b^2\right)$ and $4\left(a^2-\frac{2}{3}{b}^2\right)$

Answer 1

Multiply the binomials

$(\frac{3}{4}{a}^2+3b^2)(a^2-\frac{2}{3}{b}^2)$

$=\frac{3}{4}{a}^2(a^2-\frac{2}{3}{b}^2)+3b^2(a^2-\frac{2}{3}{b}^2)$

$=\frac{3}{4}{a}^4-\frac{1}{2}{a}^2{b}^2+3a^2{b}^2-2b^4$

$=\frac{3}{4}{a}^4-2b^4+\frac{5}{2}{a}^2{b}^2$