**Solution:**

To prove that ( *a* – *b* ) is a factor of ( *a* ^{n }– *b* ^{n }), we have to first proved that

*a* ^{n }– *b* ^{n }= *k* ( *a* – *b* ), where *k* is some natural number

It can be written that, *a* = *a* – *b* + *b*

**This shows that ( ***a* – *b* ) is a factor of ( *a* ^{n }– *b* ^{n }), where *n* is a positive integer.