Check if the following is true.$ (x+y)^{2}=(x-y)^{2}+4 x y $

Given:

\( (x+y)^{2}=(x-y)^{2}+4 x y \)

To do:

We have to check whether the given statement is true.

Solution:

LHS $=(x+y)^{2}$

$=x^2+2\times x \times y+y^2$                   [Since $(a+b)^2=a^2+2ab+b^2$]

$=x^2+2xy+y^2$

RHS $=(x-y)^{2}+4 x y$                           

$=x^2-2\times x \times y+y^2+4xy$                 [Since $(a-b)^2=a^2-2ab+b^2$]

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

$=x^2+y^2+2xy$

$=(x+y)^2$

LHS $=$ RHS

Therefore, the given statement is true.

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Updated on: 10-Oct-2022

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