- #1

DavidSnider

Gold Member

- 502

- 143

## Homework Statement

Prove x

^{n}- y

^{n}= (x-y)(x

^{n-1}+ x

^{n-2}y + ... + xy

^{n-2}+ y

^{n-1})

## Homework Equations

See Above

## The Attempt at a Solution

The previous problem in the book was:

Prove:

x

^{3}- y

^{3}= (x - y)(x

^{2}+ xy + y

^{2})

(x - y)(x

^{2}+ xy + y

^{2})

(x)(x

^{2 }+ xy + y^

^{2}) + (-y)(x

^{2}+ xy + y

^{2})

(x

^{3}+ x

^{2}y + xy

^{2}) + (-x

^{2}y - xy

^{2}- y

^{3})

x

^{3}+ x

^{2}y + xy

^{2}- x

^{2}y - xy

^{2}- y

^{3}

x

^{3}- y

^{3 }

I'm not sure how to show the same thing when the exponent is variable though.