Factorise the following by using suitable identities.$(x+y)^2- (x-y)^2$

Given:

$(x+y)^2- (x-y)^2$

To do:

We have to factorise the given expression using suitable identities.

Solution:

We know that,

$a^2-b^2=(a-b)(a+b)$

Therefore,

$(x+y)^2- (x-y)^2=[(x+y)-(x-y)][(x+y)+(x-y)]$

$=(x+y-x+y)(x+y+x-y)$

$=(2y)(2x)$

$=4xy$

Therefore, $(x+y)^2- (x-y)^2=4xy$.