Question
Simplify (xy+yz)2−2x2y2z and find it's value when x=−1,y=1 and z=2.
Answer: Option C
:
C
(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)2−2x2y2z=x2y2+y2z2+2xzy2−2x2y2z
Substitutingthe values of x,y and z in the above expression, we get
x2y2+y2z2+2xzy2−2x2y2z
(−1)2(1)2+(1)2(2)2+2(−1)(2)(1)2−2(1)2(1)2(2)
1 +4 - 4 - 4 = -3
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:
C
(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)2−2x2y2z=x2y2+y2z2+2xzy2−2x2y2z
Substitutingthe values of x,y and z in the above expression, we get
x2y2+y2z2+2xzy2−2x2y2z
(−1)2(1)2+(1)2(2)2+2(−1)(2)(1)2−2(1)2(1)2(2)
1 +4 - 4 - 4 = -3
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