SOLUTION: factor the polynomial. 8u^3-125w^3

Question 371233: factor the polynomial. 8u^3-125w^3
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

When factoring always start with the Greatest Common Factor (GCF). However the GCF here is 1 and we do not often factor out 1's. After the GCF you try any of the other factoring techniques:

Factoring by patterns
Trinomial factoring
Factoring by grouping
Factoring by trial and error of the possible rational roots.

The keys to factoring this expression are:

Recognizing that and are both perfect cubes. and
Knowing that there is a pattern for a difference of cubes:

From this we realize that we can use the pattern, with "a" being 2u and "b" being 5w:

which simplifies to:

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