If you have trouble with the math on a problem like this, you can also do some trickery with the statements.
Notice that statement 1 already give us the info in statement 2. In other words, if x+y=0, then (x+y)(x-y) will have to equal 0 as well. That means that we can rule out B and C as answers. B is out because if statement 2 is sufficient, then statement 1, which gives the same info with more specifics (we know which term is 0), can't be insufficient. C is out because we can figure s2 out for ourselves from statement 1 alone. Therefore, there's no need to combine.
That leaves us with A, D, and E. So we're faced with a simpler decision. Can we solve from knowing that x^2 -y^2 = 0? If so, the answer is D. Do we need to know specifically that x+y=0? If so, then A is the answer. Is even that not enough? Then we go with E.
If you're curious, x^ + y^3 factors to (x+y)(x^2 -xy +y^2), so if we know x+y=0, then we know the whole thing is 0.
(Notice that the longer term is NOT equal to (x-y)^2, which has -2xy in the middle, not just -xy.)
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