Science
General
Easy
Question
What is the expansion of the series (xy + 2)2?
- x2 + y2 + 4
- xy2 + 4 +2xy
- x2y2 + 2xy + 4
- x2y2 + 4xy + 4
The correct answer is: x2y2 + 4xy + 4
(a + b)2 can be expanded using the binomial theorem to get:
(a + b)2 = a2 + 2ab + b2
Here, a = xy and b = 2
Therefore, (xy + 2)2 = (xy)2 + 2(xy)(2) + (2)2
(xy + 2)2 = x2y2 + 4xy + 4.
Therefore, (xy + 2)2 = (xy)2 + 2(xy)(2) + (2)2
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