- #1
rocomath
- 1,755
- 1
Prove the following:
[tex]x^n - y^n = (x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1})[/tex]
Hmm ... I factored x then -y and came out with:
[tex]x^{n}+...x^{2}y^{n-2}-x^{n-2}y^{2}...-y^{n}[/tex]
Argh. What's up with the middle part? I'm not sure where to go from here.
[tex]x^n - y^n = (x-y)(x^{n-1}+x^{n-2}y+...+xy^{n-2}+y^{n-1})[/tex]
Hmm ... I factored x then -y and came out with:
[tex]x^{n}+...x^{2}y^{n-2}-x^{n-2}y^{2}...-y^{n}[/tex]
Argh. What's up with the middle part? I'm not sure where to go from here.
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