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

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Question 371233: factor the polynomial. 8u^3-125w^3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
8u%5E3-125w%5E3
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:
  1. Recognizing that 8u%5E3 and 125w%5E3 are both perfect cubes. 8u%5E3+=+%282u%29%5E3 and 125w%5E3+=+%285w%29%5E3
  2. Knowing that there is a pattern for a difference of cubes: a%5E3+-+b%5E3+=+%28a-b%29%28a%5E2+%2B+ab+%2B+b%5E2%29

From this we realize that we can use the pattern, with "a" being 2u and "b" being 5w:
%282u-5w%29%28%282u%29%5E2+%2B+%282u%29%285w%29+%2B+%285w%29%5E2%29
which simplifies to:
%282u-5w%29%284u%5E2+%2B+10uw+%2B+25w%5E2%29