Question

(x+y)^2-(x-y)^2=4xy identity is the equation? Write logically.

Answer 1

Hello user

Expanding the LHS we get

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

x^2+y^2 +2xy -x^2-y^2 +2xy

4xy

=RHS

Hence proved

Answer 2

$(x+y)^2-(x-y)^2=4xy$, verified.

Step-by-step explanation:

We have,

$(x+y)^2-(x-y)^2=4xy$

Verify, $(x+y)^2-(x-y)^2=4xy$

L.H.S.$=(x+y)^2-(x-y)^2$

Using algebraic identity,

$(a+b)^{2}=a^{2}+b^{2}+2ab$ and

$(a-b)^{2}=a^{2}+b^{2}-2ab$

$=(x^{2}+y^{2}+2xy)-(x^{2}+y^{2}-2xy)$

$=x^{2}+y^{2}+2xy-x^{2}-y^{2}+2xy$

$=2xy+2xy$

= 4xy

= R.H.S., verified.

Hence, $(x+y)^2-(x-y)^2=4xy$, verified.