Question

Question 1(vi)
Multiply the binomials:
$(\frac{3}{4}{a}^2+3b^2)and4(a^2-\frac{2}{3}{b}^2)$

Answer 1

$(\frac{3}{4}{a}^2+3b^2)\times 4(a^2-\frac{2}{3}{b}^2)=(\frac{3}{4}{a}^2+3b^2)\times (4a^2-\frac{8}{3}{b}^2)$
$\frac{3}{4}{a}^2\times (4a^2-\frac{8}{3}{b}^2)+3b^2\times (4a^2-\frac{8}{3}{b}^2)$
$\frac{3}{4}{a}^2\times 4a^2-\frac{3}{4}{a}^2\times \frac{8}{3}{b}^2+3b^2\times 4a^2-3b^2\times \frac{8}{3}{b}^2$
$=3a^4-2a^2{b}^2+12a^2{b}^2-8b^4$
$=3a^4+10a^2{b}^2-8b^4$