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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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