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Question

Simplify (xy+yz)2−2x2y2z and find it's value when x=−1,y=1 and z=2.


A

3

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B

4

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C

-3

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D

0

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Solution

The correct option is C

-3


(xy+yz)2 is in the form of (a+b)2 where a=xy and b=yz.
Using (a+b)2=a2+b2+2ab,
(xy+yz)2=x2y2+y2z2+2xzy2.

Therefore,
(xy+yz)22x2y2z=x2y2+y2z2+2xzy22x2y2z

Substituting the values of x,y and z in the above expression, we get
x2y2+y2z2+2xzy22x2y2z
(1)2(1)2+(1)2(2)2+2(1)(2)(1)22(1)2(1)2(2)
1 + 4 - 4 - 4 = -3


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