SOLUTION: Complete factoring! p^3-4q^2+p^2-8q^3

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Question 255485: Complete factoring!
p^3-4q^2+p^2-8q^3
Found 2 solutions by Edwin McCravy, ankor@dixie-net.com:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
p%5E3-4q%5E2%2Bp%5E2-8q%5E3

p%5E3%2Bp%5E2-4q%5E2-8q%5E3

p%5E3-8q%5E3%2Bp%5E2-4q%5E2%29

%28p%5E3-8q%5E3%29%2B%28p%5E2-4q%5E2%29

Factor the first parentheses as the difference
of two cubes and the second as the difference of two
squares:

%28p%5E3-%282q%29%5E3%29%2B%28p%5E2-%282q%29%5E2%29

%28p-2q%29%28p%5E2%2B2pq%2B4q%5E2%29%2B%28p-2q%29%28p%2B2q%29

Now notice the red factors are the same:

red%28%28p-2q%29%29%28p%5E2%2B2pq%2B4q%5E2%29%2Bred%28%28p-2q%29%29%28p%2B2q%29

so I can factor out the common red factor:

red%28%28p-2q%29%29%28%28p%5E2%2B2pq%2B4q%5E2%29%2B%28p%2B2q%29%29


%28p-2q%29%28p%5E2%2B2pq%2B4q%5E2%2Bp%2B2q%29

Edwin

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Complete factoring!
p%5E3-4q%5E2%2Bp%5E2-8q%5E3
Group like terms
p%5E3+%2B+p%5E2+-+8q%5E3+-+4q%5E2
Factor
p%5E2%28p+%2B+1%29+-+4q%5E2%282q+%2B+1%29