SOLUTION: Hello. I'm having some difficulty with the following problem. Factor each expression, if possible (c-d)r^3-(c-d)s^3 thanks!

Algebra ->  Equations -> SOLUTION: Hello. I'm having some difficulty with the following problem. Factor each expression, if possible (c-d)r^3-(c-d)s^3 thanks!      Log On


   

Question 184058: Hello.
I'm having some difficulty with the following problem.
Factor each expression, if possible
(c-d)r^3-(c-d)s^3
thanks!
Found 2 solutions by tvandenberg, jim_thompson5910:
Answer by tvandenberg(45) About Me  (Show Source):
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28c-d%29r%5E3-%28c-d%29s%5E3 Start with the given expression.


Let z=c-d


zr%5E3-zs%5E3 Replace each c-d term with "z"



z%28r%5E3-s%5E3%29 Factor out the GCF "z"



z%28r-s%29%28r%5E2%2Brs%2Bs%5E2%29 Factor r%5E3-s%5E3 by the difference of cubes formula. Note: let me know if you need help with this part.


%28c-d%29%28r-s%29%28r%5E2%2Brs%2Bs%5E2%29 Plug in z=c-d



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Answer:


So %28c-d%29r%5E3-%28c-d%29s%5E3 completely factors to %28c-d%29%28r-s%29%28r%5E2%2Brs%2Bs%5E2%29