SOLUTION: factor completely 27x^3+1

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: factor completely 27x^3+1       Log On


   

Question 280210: factor completely 27x^3+1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

27x%5E3%2B1 Start with the given expression.


%283x%29%5E3%2B%281%29%5E3 Rewrite 27x%5E3 as %283x%29%5E3. Rewrite 1 as %281%29%5E3.


%283x%2B1%29%28%283x%29%5E2-%283x%29%281%29%2B%281%29%5E2%29 Now factor by using the sum of cubes formula. Remember the sum of cubes formula is A%5E3%2BB%5E3=%28A%2BB%29%28A%5E2-AB%2BB%5E2%29


%283x%2B1%29%289x%5E2-3x%2B1%29 Multiply

-----------------------------------
Answer:

So 27x%5E3%2B1 factors to %283x%2B1%29%289x%5E2-3x%2B1%29.


In other words, 27x%5E3%2B1=%283x%2B1%29%289x%5E2-3x%2B1%29