hi guys.. exams is in a few days need help on this topic!

can i know how do i solve these questions?

Q: Prove that the following inequalities hold for all n ∈ N.

1. $\displaystyle (1+x)^n\geq1+nx $ if $\displaystyle x\geq-1$

2. $\displaystyle 1^3+2^3+...+(n-1)^3 < \frac{1}{4}n^4 < 1^3+2^3+ ... +n^3$

and one more question on mathematical induction..

Q: Prove by induction that the following statement is true for every positive integer n.

$\displaystyle x-y $ is a factor of $\displaystyle x^n - y^n $

thanks in advance!!