SOLUTION: 49a^7-9a^5

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Question 168156: 49a^7-9a^5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
49a%5E7-9a%5E5 Start with the given expression


a%5E5%2849a%5E2-9%29 Factor out the GCF a%5E5


Now let's focus on the inner expression 49a%5E2-9




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49a%5E2-9 Start with the given expression.


%287a%29%5E2-9 Rewrite 49a%5E2 as %287a%29%5E2.


%287a%29%5E2-%283%29%5E2 Rewrite 9 as %283%29%5E2.


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


%287a%2B3%29%287a-3%29 Factor the expression using the difference of squares.


So 49a%5E2-9 factors to %287a%2B3%29%287a-3%29.



So this means that a%5E5%2849a%5E2-9%29 factors to a%5E5%287a%2B3%29%287a-3%29.

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Answer:


So 49a%5E7-9a%5E5 completely factors to a%5E5%287a%2B3%29%287a-3%29