SOLUTION: Factor: 4p2 - 25

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Question 618191: Factor: 4p2 - 25
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4p%5E2-25 Start with the given expression.


%282p%29%5E2-25 Rewrite 4p%5E2 as %282p%29%5E2.


%282p%29%5E2-%285%29%5E2 Rewrite 25 as %285%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=2p and B=5.


So let's use the difference of squares formula A%5E2-B%5E2=%28A%2BB%29%28A-B%29 to factor the expression:


A%5E2-B%5E2=%28A%2BB%29%28A-B%29 Start with the difference of squares formula.


%282p%29%5E2-%285%29%5E2=%282p%2B5%29%282p-5%29 Plug in A=2p and B=5.


So this shows us that 4p%5E2-25 factors to %282p%2B5%29%282p-5%29.


In other words 4p%5E2-25=%282p%2B5%29%282p-5%29.