Question

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

• A. $3a^4+10a{b}^2-8b^4$
• B. $3a^4+10a^2{b}^2-4b^4$
• C. $4a^4+10a^2{b}^2-8b^4$
• D. $3a^4+10a^2{b}^2-8b^4$

Answer 1

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

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