Question

What is the answer of \(\frac{x^2+y^2+2xy}{x^2-y^2}\)?

(a) (x – y) (x + y)^-2

(b) (x + y) (x – y)^-2

(c) (x + y) (x – y)^-1

(d) (x – y) (x + y)^-1

I have been asked this question during an interview.

This key question is from Binomial Theorem for Positive Integral Index topic in section Binomial Theorem of Mathematics – Class 11

Answer 1

The correct answer is (c) (x + y) (x – y)^-1

The explanation: x^2 + y^2 + 2xy is the expansion of (x + y)^2

x^2 – y^2 can be written as (x – y)(x + y)

Substituting in the fraction we get, \(\frac{(x + y)^2}{(x – y)(x + y)}\).

After cancelling the terms we get, \(\frac{x^2+y^2+2xy}{x^2-y^2}\) = (x + y) (x – y)^-1.