SOLUTION: Please help factor: {{{(3x+1)^6(2x-5)^0.5+(2x-5)^1.5(3x+1)^5}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help factor: {{{(3x+1)^6(2x-5)^0.5+(2x-5)^1.5(3x+1)^5}}}      Log On


   

Question 158082: Please help factor: %283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
%283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5

Substitute A for %283x%2B1%29
Substitute B for %282x-5%29

Then

%283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5

becomes:

A%5E6%2AB%5E0.5%2BB%5E1.5%2AA%5E5 

Factor out the smaller power of A which is A%5E5
Factor out the smaller power of B which is B%5E0.5

A%5E5%2AB%5E0.5%28A%5E1%2BB%5E1%29

A%5E5%2AB%5E0.5%28A%2BB%29

Replace A by %283x%2B1%29
Replace B by %282x-5%29

%283x%2B1%29%5E5%282x-5%29%5E0.5%28%283x%2B1%29%2B%282x-5%29%29

+%283x%2B1%29%5E5%282x-5%29%5E0.5%283x%2B1%2B2x-5%29+

+%283x%2B1%29%5E5%282x-5%29%5E0.5%285x-4%29+

Edwin