If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer? Choose the correct choice from the following answers
A) 1/2  B) 1/3  C) 1/4  D) 1/5  E) 1/6
There are total 4C2=64C2=6 ways to choose 2 equations out of 4 at random.   We want the product of 2 equations in format x2−(by)2x2−(by)2, where b is a constant coefficient of term y2y2. Also note equation does not contain any xyxy term.   There are only 2 equations, (x+y) &amp; (x-y) which gives the product x2−y2x2−y2. Product of all other equations will contain term xyxy   So answer = 1/6   ANS:1/6
<result>E</result>
If two of the four expressions x+y, x+5y, x-y, 5x+y are chosen at random, what is the probability that their product will be of the form of x^2 - (by)^2, where b is an integer?