SOLUTION: I need help solving a problem that I was told to use the cubic special product pattern. {{{p^3+6p^2q+12pq^2+8q^3}}} I started by using grouping, but I really am not sure what

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I need help solving a problem that I was told to use the cubic special product pattern. {{{p^3+6p^2q+12pq^2+8q^3}}} I started by using grouping, but I really am not sure what      Log On


   

Question 376644: I need help solving a problem that I was told to use the cubic special product pattern.
p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3
I started by using grouping, but I really am not sure what the cubic special product pattern is.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is a bit tricky as you're going to use multiple factoring methods (and a bit of creativity).


p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3 Start with the given expression.


p%5E3%2B8q%5E3%2B6p%5E2q%2B12pq%5E2 Rearrange the terms where the cubic terms are the first two terms.


%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%29%2B6pq%28p%2B2q%29 Factor p%5E3%2B8q%5E3 using the sum of cubes formula and factor out the GCF 6pq from the last two terms.


%28p%2B2q%29%28p%5E2-2pq%2B4q%5E2%2B6pq%29 Now factor out the GCF p%2B2q from the entire expression.


%28p%2B2q%29%28p%5E2%2B4pq%2B4q%5E2%29 Combine like terms.


%28p%2B2q%29%28p%2B2q%29%28p%2B2q%29 Factor p%5E2%2B4pq%2B4q%5E2 to get %28p%2B2q%29%28p%2B2q%29


%28p%2B2q%29%5E3 Condense the factors.


So p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3 completely factors to %28p%2B2q%29%5E3


In other words, p%5E3%2B6p%5E2q%2B12pq%5E2%2B8q%5E3=%28p%2B2q%29%5E3


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim