SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{27p^3-1}}} I really appriciate it. I am not getting this section at all.

Algebra ->  Functions -> SOLUTION: Can you help me solve the following problem. It is to Factor the polynomial completely. {{{27p^3-1}}} I really appriciate it. I am not getting this section at all.      Log On


   

Question 121494: Can you help me solve the following problem. It is to Factor the polynomial completely.
27p%5E3-1
I really appriciate it. I am not getting this section at all.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

27p%5E3-1 Start with the given expression.


%283p%29%5E3-%281%29%5E3 Rewrite 27p%5E3 as %283p%29%5E3. Rewrite 1 as %281%29%5E3.


%283p-1%29%28%283p%29%5E2%2B%283p%29%281%29%2B%281%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%283p-1%29%289p%5E2%2B3p%2B1%29 Multiply

-----------------------------------
Answer:
So 27p%5E3-1 factors to %283p-1%29%289p%5E2%2B3p%2B1%29.

In other words, 27p%5E3-1=%283p-1%29%289p%5E2%2B3p%2B1%29