SOLUTION: Complete the proof (a exponent3 + b exponent 3)*(a+b)=a exponent2 - ab+b exponent 2

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Question 133453: Complete the proof
(a exponent3 + b exponent 3)*(a+b)=a exponent2 - ab+b exponent 2
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot prove %28a%5E3%2Bb%5E3%29%2A%28a%2Bb%29=%28a%5E2-ab%2Bb%5E2%29, at least not in general. There may be some values of a and b for which this relationship holds, such as a = 0 and b = 1 for example, but it is not true for every real value of a and b. If a = 1 and b = 1, then %281%2B1%29%281%2B1%29=2%2A2=4%3C%3E%281-1%2B1%29=1

I suspect that you just weren't being careful when you typed the problem and you really meant:

%28a%5E3%2Bb%5E3%29=%28a%2Bb%29%2A%28a%5E2-ab%2Bb%5E2%29

This relationship IS true for all real a, b, and it can be proven by multiplying the two polynomials on the right of the equation and demonstrating that the result is identical to the left side:



If you are required to do a rigorous proof with reasons for the steps, then the first reason is the distributive property and the second is the additive inverse property.