SOLUTION: Factor the binomial 81m^4-625

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Question 190660: Factor the binomial
81m^4-625
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

81m%5E4-625 Start with the given expression.


%289m%5E2%29%5E2-625 Rewrite 81m%5E4 as %289m%5E2%29%5E2.


%289m%5E2%29%5E2-%2825%29%5E2 Rewrite 625 as %2825%29%5E2.


Notice how we have a difference of squares A%5E2-B%5E2 where in this case A=9m%5E2 and B=25.


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.


%289m%5E2%29%5E2-%2825%29%5E2=%289m%5E2%2B25%29%289m%5E2-25%29 Plug in A=9m%5E2 and B=25.


So this shows us that 81m%5E4-625 factors to %289m%5E2%2B25%29%289m%5E2-25%29.


In other words 81m%5E4-625=%289m%5E2%2B25%29%289m%5E2-25%29.


Now let's factor 9m%5E2-25


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


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


%283m%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=3m 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.


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


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


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

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So 81m%5E4-625 completely factors to %289m%5E2%2B25%29%283m%2B5%29%283m-5%29


In other words, 81m%5E4-625=%289m%5E2%2B25%29%283m%2B5%29%283m-5%29