Question

Divide and verify.

$\frac{4}{3}{x}^2{b}^2$ by $\frac{16}{3}{b}^3$

Answer 1

Step 1: Divide $\frac{4}{3}{x}^2{b}^2$ by $\frac{16}{3}{b}^3$

Consider $\frac{4}{3}{x}^2{b}^2$ by $\frac{16}{3}{b}^3$ i.e,

$\frac{16}{3}{b}^3\frac{x^2}{4b}\frac{4}{3}{x}^2{b}^2\frac{4}{3}{x}^2{b}^2—0—$

Now, the division of $\frac{4}{3}{x}^2{b}^2$ by $\frac{16}{3}{b}^3$ is $\frac{x^2}{4b}$

Step 2: Find the dividend

We know that

$$\begin{gathered} Dividend=Divisior\times Quotient+Remainder \\ \frac{4}{3}{x}^2{b}^2=\frac{16}{3}{b}^3\times \frac{1}{4b}{x}^2 \\ \frac{4}{3}{x}^2{b}^2=\frac{4}{3}{x}^2{b}^2 \end{gathered}$$

Hence, verified.