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

Step 1: Follow the following steps to multiply two binomials.

• Apply the distributive law of multiplication.
• Multiply every term of one binomial with every term in the other binomial.
• Look for like terms, if any, and combine them.

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

$\begin{array}{l}\left(\frac{3}{4}{a}^2+3b^2\right)\times 4\left(a^2-\frac{2}{3}{b}^2\right)\\ =\left(\frac{3}{4}{a}^2+3b^2\right)\times \left(4a^2-\frac{8}{3}{b}^2\right)\\ =\frac{3}{4}{a}^2\left(4a^2-\frac{8}{3}{b}^2\right)+3b^2\left(4a^2-\frac{8}{3}{b}^2\right)\\ =3a^4-2a^2{b}^2+12a^2{b}^2-8b^4\\ =3a^4+10a^2{b}^2-8b^4\end{array}$

Hence the product of $\left(\frac{3}{4}{a}^2+3b^2\right)$ and$4\left(a^2-\frac{2}{3}{b}^2\right)$ is $3a^4+10a^2{b}^2-8b^4$.