Question

$\text{Factorise:}(2l+m{)}^2-8lm$

• A. $(2m-l{)}^2$
• B. $(2m+l{)}^2$
• C. $(2l+m{)}^2$
• D. $(2l-m{)}^2$

Answer 1

The correct option is D $(2l-m{)}^2$

$\text{Given:}(2l+m{)}^2-8lm$

$\text{On expanding}(2l+m{)}^2\text{using the}\text{identity}(a+b{)}^2=a^2+2ab+b^2,\text{we get,}$
$(2l+m{)}^2=(2l{)}^2+4lm+m^2$

$\text{So,}(2l+m{)}^2-8lm=(2l{)}^2+4lm+m^2-8lm=(2l{)}^2+(-4lm)+m^2$

$\text{By comparing this with the same}\text{identity}(a+b{)}^2=a^2+2ab+b^2,a=2l,b=-m(2l+m{)}^2-8lm=(2l-m{)}^2$