Question

Multiply the binomials

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

• A. $3a^4+10a^2{b}^2-8b^4$
• B. $3a^4+12a^2{b}^2-8b^4$
• C. $3a^4+10a^2{b}^2+8b^4$
• D. None of these

Answer 1

The correct option is A $3a^4+10a^2{b}^2-8b^4$

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

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

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

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

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