Hi. I was trying to solve the quant challenge for september 16, 2002 called 'Complex Simplification' (http://www.manhattangmat.com/ChallengeP ... ChallID=66) and apparently I'm doing something wrong with the simplification, I just don't know what. Can you help me?
Stem is:
8xy^3 + 8x^3y = {2x^2y^2}/2^-3
So I simplified:
8xy(y^2 + x^2) = 2^3(2x^2y^2)
8xy(y^2 + x^2) = 8(2)(x^2)(y^2)
8xy(y^2 + x^2) = 8(2)(x)(x)(y)(y), therefore 8xy(2xy) <===== I'm guessing this is where I'm wrong. Is this a valid operation?
y^2 + x^2 = 2xy
y^2 + -2xy + x^2 = 0
(y-x)(y-x)=0
y=x
I followed your explanation and it makes sense but I can't explain what's wrong with my simplification.
Btw, MGMAT's answer is:
xy(y^2 + -2xy + x^2) = 0
xy (y-x)(y-x) = 0
xy = 0
-or-
y=x
Thanks in advance!