SOLUTION: please prove.. if a>b then a^3>b^3

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Question 460861: please prove..
if a>b then a^3>b^3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
a%5E2%2Bab%2Bb%5E2=%28%28a%2B%28b%2F2%29%29%5E2%2B3b%5E2%2F4%29
but if a%3Eb then a-b%3E0 and clearly a%2B%28b%2F2%29%5E2%3E0 and 3b%5E2%2F4%3E0
so, %28a-b%29%28a%5E2%2Bab%2Bb%5E2%29%3E0, hence a%5E3-b%5E3%3E0 and a%5E3%3Eb%5E3