Question

Using special products, simplify :

${(2x-3y)}^2$

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 $a=2x,b=3y$

Step 2: Applying the formula

$$\begin{gathered} {(2x-3y)}^2={\left(2x\right)}^2-2\left(2x\right)\left(3y\right)+{\left(3y\right)}^2 \\ =4x^2-12xy+{9y}^2 \end{gathered}$$

Hence, the square of ${(2x-3y)}^2$ is $4x^2-12xy+{9y}^2$.