/sci/ - Science & Math

From Spivak's Callculus 1.1.5:
>[math] (x^2 + X^{n-1}y +...+x^2 y^{n-2} + y^{n-1}x) - (yx^{n-1} - y^2x^{n-2} -...- xy^{n-1} - y^n) [/math]

Which readily simplifies to:
>[math] x^n + x^2y^{n-2} - x^{n-2}y^2 + y^n [/math]

But the answer is supposed to be [math] x^n + y^n [/math], and I'm failing to see how to simplify further. Is it something to do with the expansion in the ellipses? I'm having the same problem this guy is: https://math.stackexchange.com/questions/580397/spivak-calculus-chapter-1-problem-1v


It seems the top answer by 'oks' simply continued the expansion for one more step, is this the solution?