Simplify, and write without negative exponents?

Question

$(x^(n-1) + y^(n-2))(x^n + y^(n-1))$

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Answer 1 · 2016-12-07T13:57:23

$(x^(2n))/x + (x^ny^n)/(xy) + (x^ny^n)/y^2 + y^(2n)/y^3$

The first step is to cross multiple the terms in parenthesis:

$x^(n-1)x^n + x^(n-1)y^(n-1) + x^ny^(n-2) + y^(n-2)y^(n-1)$

$x^(n-1 + n) + x^(n-1)y^(n-1) + x^ny^(n-2) + y^(n-2 + n - 1)$

$x^(2n-1) + x^(n-1)y^(n-1) + x^ny^(n-2) + y^(2n-3)$

Now we can work with the negative portion of the exponents.

$x^(2n)x^(-1) + x^nx^(-1)y^ny^-1 + x^ny^ny^-2 + y^(2n)y^-3$

$(x^(2n))/x + (x^ny^n)/(xy) + (x^ny^n)/y^2 + y^(2n)/y^3$