# Simplify, and write without negative exponents?

## $\left({x}^{n - 1} + {y}^{n - 2}\right) \left({x}^{n} + {y}^{n - 1}\right)$

Dec 7, 2016

$\frac{{x}^{2 n}}{x} + \frac{{x}^{n} {y}^{n}}{x y} + \frac{{x}^{n} {y}^{n}}{y} ^ 2 + {y}^{2 n} / {y}^{3}$

#### Explanation:

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

${x}^{n - 1} {x}^{n} + {x}^{n - 1} {y}^{n - 1} + {x}^{n} {y}^{n - 2} + {y}^{n - 2} {y}^{n - 1}$

${x}^{n - 1 + n} + {x}^{n - 1} {y}^{n - 1} + {x}^{n} {y}^{n - 2} + {y}^{n - 2 + n - 1}$

${x}^{2 n - 1} + {x}^{n - 1} {y}^{n - 1} + {x}^{n} {y}^{n - 2} + {y}^{2 n - 3}$

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

${x}^{2 n} {x}^{- 1} + {x}^{n} {x}^{- 1} {y}^{n} {y}^{-} 1 + {x}^{n} {y}^{n} {y}^{-} 2 + {y}^{2 n} {y}^{-} 3$

$\frac{{x}^{2 n}}{x} + \frac{{x}^{n} {y}^{n}}{x y} + \frac{{x}^{n} {y}^{n}}{y} ^ 2 + {y}^{2 n} / {y}^{3}$