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

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


   

Question 158085: Please help solve: %283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: this is not an equation, so you can only simplify it (not solve it)


Notice how %282x-5%29%5E0.5=%282x-5%29%5E%281%2F2%29 and %282x-5%29%5E1.5=%282x-5%29%5E%283%2F2%29


Remember, x%5E%281%2F2%29=sqrt%28x%29. So this means that %282x-5%29%5E%281%2F2%29=sqrt%282x-5%29 and %282x-5%29%5E%283%2F2%29=%28sqrt%282x-5%29%29%5E3



So what this means is that the expression %283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5 becomes


%283x%2B1%29%5E6%2Asqrt%282x-5%29%2B%28sqrt%282x-5%29%29%5E3%283x%2B1%29%5E5


Now let z=sqrt%282x-5%29 and w=3x%2B1 to transform the expression into


w%5E6%2Az%2Bz%5E3w%5E5


w%5E5%2Az%28w%2Bz%5E2%29 factor out the GCF w%5E5%2Az


%283x%2B1%29%5E5%2Asqrt%282x-5%29%28%283x%2B1%29%2B%28sqrt%282x-5%29%29%5E2%29 Plug in z=sqrt%282x-5%29 and w=3x%2B1


%283x%2B1%29%5E5%2Asqrt%282x-5%29%28%283x%2B1%29%2B2x-5%29 Square sqrt%282x-5%29 to get 2x-5


%283x%2B1%29%5E5%2Asqrt%282x-5%29%285x-4%29 Combine like terms.


%283x%2B1%29%5E5%2A%285x-4%29%2Asqrt%282x-5%29 Rearrange the terms.


So %283x%2B1%29%5E6%282x-5%29%5E0.5%2B%282x-5%29%5E1.5%283x%2B1%29%5E5 simplifies to %283x%2B1%29%5E5%2A%285x-4%29%2Asqrt%282x-5%29