Question

Evaluate :
(i) $(2x+3y{)}^2$ (ii) $(2x-3y{)}^2$ (iii) $(2x+3y)(2x-3y)$

Answer 1

(i) We have,
$(2x+3y{)}^2=(2x{)}^2+2\times \left(2x\right)\times \left(3y\right)+(3y{)}^2$ [Using : $(a+b{)}^2=a^2+2ab+b^2$]
= $4x^2+12xy+9y^2$

(ii) We have,
$(2x-3y{)}^2=(2x{)}^2-2\times \left(2x\right)\times \left(3y\right)+(3y{)}^2$ [Using : $(a-b{)}^2=a^2-2ab+b^2$]
= $4x^2-12xy+9y^2$

(iii) We have,
$(2x+3y)(2x-3y)=(2x{)}^2-(3y{)}^2$ [Using : $(a+b)(a-b)=a^2-b^2$]
$4x^2-9y^2$.