SOLUTION: In an algebra review packet that I was assigned we are supposed to factor completely the special products that we are given. The solutions are given but there is no explanation.

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Question 481989: In an algebra review packet that I was assigned we are supposed to factor completely the special products that we are given. The solutions are given but there is no explanation.
The question: x^3 -27
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3-27 Start with the given expression.


%28x%29%5E3-%283%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 27 as %283%29%5E3.


%28x-3%29%28%28x%29%5E2%2B%28x%29%283%29%2B%283%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28x-3%29%28x%5E2%2B3x%2B9%29 Multiply

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Answer:

So x%5E3-27 factors to %28x-3%29%28x%5E2%2B3x%2B9%29.


In other words, x%5E3-27=%28x-3%29%28x%5E2%2B3x%2B9%29