Question

Factorise:
(l + m)² − 4lm

Answer 1

We have:
${\left(l+m\right)}^2-4lm=\left(l^2+m^2+2lm\right)-4lm$
$$\begin{gathered} =l^2+m^2+2lm-4lm \\ =l^2+m^2-2lm \\ ={\left(l\right)}^2+{\left(m\right)}^2-2\times l\times m \\ ={\left(l-m\right)}^2 \end{gathered}$$

∴ ${\left(l+m\right)}^2-4lm={\left(l-m\right)}^2$