If f(x+2y,x-2y)=xy, then f(x,y) equals

(A)(x²-y²)÷8 (B)(x²-y²)÷4 (C) (x²+y²)÷4

(D)(x²-y²)/2

I first worked it backwards. I start with f(x,y) = (x^2 - y^2)/8. Then I substitute x+2y for x and x-2y for y. Do the algebra and get xy. This proves the converse of the problem.

Now run it forwards: f(x+2y, x-2y) = xy = 8xy/8 = ( (x^2 + 4xy + 4y^2) - (x^2 - 4xy + 4y^2) ) /8 = ( (x+2y)^2 - (x-2y)^2) )/8. Substitute x for x+2y and y for x-2y and get f(x,y) = ( x^2 - y^2)/8.