SOLUTION: I just don't understand how to do this. Please help? Factor by grouping: 4p^2 - q^2 + 2p + q Thanks SO much

Algebra ->  Equations -> SOLUTION: I just don't understand how to do this. Please help? Factor by grouping: 4p^2 - q^2 + 2p + q Thanks SO much      Log On


   

Question 242949: I just don't understand how to do this. Please help?
Factor by grouping: 4p^2 - q^2 + 2p + q
Thanks SO much
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4p%5E2+-+q%5E2+%2B+2p+%2B+q Start with the given expression.


%284p%5E2+-+q%5E2%29+%2B+%282p+%2B+q%29 Group the terms into pairs


%28%282p%29%5E2+-+q%5E2%29+%2B+%282p+%2B+q%29 Rewrite 4p%5E2 as %282p%29%5E2


%282p%2Bq%29%282p-q%29+%2B+%282p+%2B+q%29 Factor the first group using the difference of squares formula.


%282p%2Bq%29%28%282p-q%29+%2B+1%29 Factor out the GCF 2p%2Bq


%282p%2Bq%29%282p-q+%2B+1%29 Remove the inner parenthesis.


So 4p%5E2+-+q%5E2+%2B+2p+%2B+q completely factors to %282p%2Bq%29%282p-q+%2B+1%29


In other words, 4p%5E2+-+q%5E2+%2B+2p+%2B+q=%282p%2Bq%29%282p-q+%2B+1%29