A basic 2-equation GMAT/GRE Problem

If `x+y=a` and `x-y=b`, then `2*x*y=`
(A) `(a^2-b^2)/2`
(B) `(b^2-a^2)/2`
(C) `(a-b)/2`
(D) `(a*b)/2`
(E) `(a^2+b^2)/2`

A classic problem that I see all the time on both the GMAT and GRE, take a look at one way to solve it:
[spoiler below]




we start out with two equations:
1: `x+y=a`
2: `x-y=b`
after squaring both sides of (1):
3: `(x+y)^2=x^2 + 2*x*y + y^2 = a^2`
after squaring both sides of (2):
4: `(x-y)^2=x^2 -2*x*y+y^2=b^2`
now lets subtract (4) from (3) to get:
5: `(x^2 + 2*x*y + y^2) - (x^2 -2*x*y+y^2) = 4*x*y = a^2 - b^2`
now if we divide both sides of (5) by 2 we get:
6: `2*x*y=(a^2-b^2)/2`

which is answer choice (A)