SOLUTION: Please help solve: {{{(a-b)^5+4(a-b)^3}}}

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Question 158080This question is from textbook Intermediate Algebra
: Please help solve: %28a-b%29%5E5%2B4%28a-b%29%5E3 This question is from textbook Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let z=a-b


So the expression %28a-b%29%5E5%2B4%28a-b%29%5E3 becomes z%5E5%2B4z%5E3


z%5E5%2B4z%5E3 Start with the given expression


z%5E3%28z%5E2%2B4%29 Factor out the GCF z%5E3


%28a-b%29%5E3%28%28a-b%29%5E2%2B4%29 Plug in z=a-b


%28a-b%29%5E3%28a%5E2-2ab%2Bb%5E2%2B4%29 FOIL


So %28a-b%29%5E5%2B4%28a-b%29%5E3 factors to %28a-b%29%5E3%2A%28a%5E2-2a%2Ab%2Bb%5E2%2B4%29

In other words, %28a-b%29%5E5%2B4%28a-b%29%5E3=%28a-b%29%5E3%2A%28a%5E2-2a%2Ab%2Bb%5E2%2B4%29