Question

What is the expansion of the series (xy + 2)^2?

(a) x^2 + y^2 + 4

(b) xy^2 + 4 +2xy

(c) x^2y^2 + 2xy + 4

(d) x^2y^2 + 4xy + 4

I had been asked this question in a national level competition.

I'd like to ask this question from Binomial Theorem for Positive Integral Index topic in chapter Binomial Theorem of Mathematics – Class 11

Answer 1

Correct choice is (d) x^2y^2 + 4xy + 4

To explain I would say: (a + b)^2 can be expanded using binomial theorem to get:

(a + b)^2 = a^2 + 2ab + b^2

Here, a = xy and b = 2

Therefore, (xy + 2)^2 = (xy)^2 + 2(xy)(2) + (2)^2

(xy + 2)^2 = x^2y^2 + 4xy + 4.