Exercise miscellaneous

If a and b are distinct integers, prove that a - b is a factor of an - bn, whenever n is a positive integer. [Hint write a n = (a - b + b)n and expand]

3 2 3 2+ − − .

2 2 2 21 1a a a a+ − + − − .

Find an approximation of (0.99)5 using the first three terms of its expansion.

Expand using Binomial Theorem 21 02 x , xx  + − ≠   .

Find the expansion of (3x2 - 2ax + 3a2)3 using binomial theorem.