If (x+2y)=a and (x-2y)=b, which of the following expression is equal to xy?

A ab

B (a+b)/2

C (a2-b2)/8

D (a2-b2)/4

Correct Answer: Option C

x+2y = a

x-2y = b

Adding above two eauations, x = a+b/2

Subtracting above two equations, y = a-b/4

so, xy = (a+b)/2 + (a-b)/4 = (a+b) (a-b)/8 = (a2 - b2)/8