1) Prove that for every x>=0 and 0<a<1

Question

x^a-ax<=1-a

2)prove that for 0<=x<=1:

x^m*(1-x)^n<= (m^m*n^n)/((m+n)^(m+n))

can someone please guide/help me in about how to solve and or approch these questions?

(I know I have already posted it before but i think it is buried beneath other questions therfore i post it again)