SOLUTION: Factor X^3-64

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Question 633627: Factor
X^3-64
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
two special factoring formulas are two sides of the same coin: the sum and
difference of cubes. These are the formulas:

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

a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29.....use this one in your case...notice that a=x and b=y
since you have x%5E3+%2B64+, your b%5E3=64, so you need to find a number whose cube is 64....it is 4, because 4%5E3=64
and your expression will be x%5E3+%2B64=x%5E3-4%5E3+
now plug it in a rule
a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
x%5E3-4%5E3=%28x-4%29%28x%5E2%2B%28-4%29x%2B4%5E2%29
or

x%5E3-4%5E3=%28x-4%29%28x%5E2-4x%2B16%29