Question

Factorise:
(l + m)² − (l − m)²

Answer 1

We have:
$$\begin{gathered} {\left(l+m\right)}^2-{\left(l-m\right)}^2=\left\{\left(l+m\right)+\left(l-m\right)\right\}\left\{\left(l+m\right)-\left(l-m\right)\right\} \\ =\left(l+m+l-m\right)\left(l+m-l+m\right) \\ =\left(2l\right)\left(2m\right) \end{gathered}$$

∴ ${\left(l+m\right)}^2-{\left(l-m\right)}^2=\left(2l\right)\left(2m\right)$