Question

Factorise: (l + m)² - (l - m)²

Answer 1

Factorise the given expression

The given expression is ,

$$\begin{gathered} {(l+m)}^2–{(l–m)}^2 \\ =\left[\right(l+m)+(l–m\left)\right]\left[\right(l+m)-(l–m\left)\right] \end{gathered}$$ {using identity $x^2–y^2=(x+y)(x–y)$}

$$\begin{gathered} =(l+m+l-m)(l+m-l+m) \\ =\left(2l\right)\left(2m\right) \\ =4ml \end{gathered}$$

Hence , the answer is $4ml$