SOLUTION: Factor Completly: 9x^4-25x^2

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Question 200145: Factor Completly: 9x^4-25x^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E4-25x%5E2 Start with the given expression


x%5E2%289x%5E2-25%29 Factor out the GCF x%5E2


Now let's focus on the inner expression 9x%5E2-25

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9x%5E2-25 Start with the given expression.


%283x%29%5E2-25 Rewrite 9x%5E2 as %283x%29%5E2.


%283x%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=3x 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.


%283x%29%5E2-%285%29%5E2=%283x%2B5%29%283x-5%29 Plug in A=3x and B=5.


So this shows us that 9x%5E2-25 factors to %283x%2B5%29%283x-5%29.


In other words 9x%5E2-25=%283x%2B5%29%283x-5%29.


This means that x%5E2%289x%5E2-25%29 factors further to x%5E2%283x%2B5%29%283x-5%29
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Answer:


So 9x%5E4-25x%5E2 completely factors to x%5E2%283x%2B5%29%283x-5%29


In other words, 9x%5E4-25x%5E2=x%5E2%2A%283x%2B5%29%2A%283x-5%29