Question

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

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

Answer 1

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

Given: $(2l+m{)}^2-8lm$.
Expand $(2l+m{)}^2$ using the identity $(a+b{)}^2=a^2+2ab+b^2$
$(2l+m{)}^2-8lm=(2l{)}^2+4lm+m^2-8lm$
$=(2l{)}^2-4lm+m^2$
Now, using the identity
$(a-b{)}^2=a^2-2ab+b^2$ we get,
$=(2l-m{)}^2$