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The value of (x+y)2+(x−y)2(x+y)^2+(x-y)^2(x+y)2+(x−y)2​​
Question

The value of (x+y)2+(xy)2(x+y)^2+(x-y)^2​​

A.

2(x+y)22 (x+y)^2​​

B.

2(x2+y2)2(x^2+y^2)​​

C.

(2x+2y)2(2x+2y)^2​​

D.

4xy

Correct option is B

Solution:

(x+y)2=x2+2xy+y2,(xy)2=x22xy+y2.Now, add the two expansions:(x+y)2+(xy)2=(x2+2xy+y2)+(x22xy+y2).(x+y)2+(xy)2=2x2+2y2.(x + y)^2 = x^2 + 2xy + y^2,\\(x - y)^2 = x^2 - 2xy + y^2.\\\text {Now, add the two expansions:}\\(x + y)^2 + (x - y)^2 = (x^2 + 2xy + y^2) + (x^2 - 2xy + y^2).\\ (x + y)^2 + (x - y)^2 = 2x^2 + 2y^2.\\


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