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"Show by induction that (1-nu)(1+u)<=1 for n=0,1,2,3... and u>-1"

For n=0:

(1-0*u)(1+u)^0 <=1

1*1<=1

1<=1, which is true.

Assume that the statement is true for n=k: (1-ku)(1+u)^k<=1

Then it follows that

(1-(k+1)u)(1+u)^(k+1) <= 1... And how do I continue? I really don't have a clue what to do now :(