Question

Simplify the following using the identities : ${(\frac{x}{4}+\frac{5}{y})}^2$

Answer 1

Step 1 : First we need to identify the identity we can use, here we need to find the square, so we can use ${(a+b)}^2=a^2+2ab+b^2$

Step 2 : Now if we compare the question with the identity we get $a=x,b=0.4y$

$$\begin{gathered} {(\frac{x}{4}+\frac{5}{y})}^2={\left(\frac{x}{4}\right)}^2+2\left(\frac{x}{4}\right)\left(\frac{5}{y}\right)+{\left(\frac{5}{y}\right)}^2 \\ =\frac{x^2}{16}+\frac{5x}{2y}+\frac{25}{y^2} \end{gathered}$$

Hence the answer of ${(\frac{x}{4}+\frac{5}{y})}^2$ is $\frac{x^2}{16}+\frac{5x}{2y}+\frac{25}{y^2}$