Question

Factorise the following expression: ${\left(l+m\right)}^2-4lm$

Answer 1

Factorise the given expression:

The given expression is,

${\left(l+m\right)}^2-4lm=l^2+m^2+2lm-4lm$. $\left[\because {\left(a+b\right)}^2=a^2+b^2+2ab\right]$

$=l^2+m^2-2lm$

$={\left(l-m\right)}^2$ $\left[\because {\left(a-b\right)}^2=a^2+b^2-2ab\right]$

Hence, the factors are $\left(l-m\right)$ and.$\left(l-m\right)$.