Question

If $x{y}^{2}k={(4xy+3y)}^2-{(4xy-3y)}^2$. Find the value of $k$.

Answer 1

Solution.

It is given that,

$$\begin{gathered} \Rightarrow x{y}^{2}k={(4xy+3y)}^2-{(4xy-3y)}^2 \\ \Rightarrow x{y}^{2}k=16x^2{y}^2+9y^2+24x{y}^2-16x^2{y}^2-9y^2+24x{y}^2\left[\mathrm{Using}{(a+b)}^2=a^2+b^2=2ab\mathrm{and}{(a-b)}^2=a^2+b^2-2ab\right] \\ \Rightarrow x{y}^{2}k=48x{y}^2 \\ \Rightarrow k=\frac{48x{y}^2}{x{y}^2} \\ \therefore k=48 \end{gathered}$$

Hence, the value of $k$is $48$.