Question

Using the identities, simplify the following :

${(3x-\frac{1}{4x})}^2$

Answer 1

Step 1: Identification of identity

First we need to identify the identity we can use,

Here we need to find the square, so we can use ${(a-b)}^2=a^2-2ab+b^2$

Now if we compare the question with the identity we get $a=3x,b=\frac{1}{4x}$

Step 2: Applying the formula

$$\begin{gathered} {(3x-\frac{1}{4x})}^2={\left(3x\right)}^2-2\left(3x\right)\left(\frac{1}{4x}\right)+{\left(\frac{1}{4x}\right)}^2] \\ =9x^2-\frac{3}{2}+\frac{1}{16x^2} \end{gathered}$$

Hence, the square of ${(3x-\frac{1}{4x})}^2$ is $9x^2-\frac{3}{2}+\frac{1}{16x^2}$.