SOLUTION: 81x^4-16

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Question 183091: 81x^4-16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

81x%5E4-16 Start with the given expression.


%289x%5E2%29%5E2-16 Rewrite 81x%5E4 as %289x%5E2%29%5E2.


%289x%5E2%29%5E2-%284%29%5E2 Rewrite 16 as %284%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9x%5E2 and B=4.


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.


%289x%5E2%29%5E2-%284%29%5E2=%289x%5E2%2B4%29%289x%5E2-4%29 Plug in A=9x%5E2 and B=4.


So this shows us that 81x%5E4-16 factors to %289x%5E2%2B4%29%289x%5E2-4%29.


In other words 81x%5E4-16=%289x%5E2%2B4%29%289x%5E2-4%29.



Now let's factor 9x%5E2-4 further

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9x%5E2-4 Start with the given expression.


%283x%29%5E2-4 Rewrite 9x%5E2 as %283x%29%5E2.


%283x%29%5E2-%282%29%5E2 Rewrite 4 as %282%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=3x and B=2.


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-%282%29%5E2=%283x%2B2%29%283x-2%29 Plug in A=3x and B=2.


So this shows us that 9x%5E2-4 factors to %283x%2B2%29%283x-2%29.


In other words 9x%5E2-4=%283x%2B2%29%283x-2%29.

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Answer:


So 81x%5E4-16 completely factors to %289x%5E2%2B4%29%283x%2B2%29%283x-2%29