SOLUTION: factor 49xy^2-25x

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Question 190752: factor
49xy^2-25x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

49xy%5E2-25x Start with the given expression


x%2849y%5E2-25%29 Factor out the GCF x


Now let's focus on the inner expression 49y%5E2-25




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49y%5E2-25 Start with the given expression.


%287y%29%5E2-25 Rewrite 49y%5E2 as %287y%29%5E2.


%287y%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=7y 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.


%287y%29%5E2-%285%29%5E2=%287y%2B5%29%287y-5%29 Plug in A=7y and B=5.


So this shows us that 49y%5E2-25 factors to %287y%2B5%29%287y-5%29.


In other words 49y%5E2-25=%287y%2B5%29%287y-5%29.

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Answer:
So 49xy%5E2-25x completely factors to x%287y%2B5%29%287y-5%29