SOLUTION: Factor Completely: 9x^9 -16x^7 + 9x^6 -16x^4

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Question 119395: Factor Completely:
9x^9 -16x^7 + 9x^6 -16x^4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
9x%5E9-16x%5E7%2B9x%5E6-16x%5E4 Start with the given expression


x%5E4%289x%5E5-16x%5E3%2B9x%5E2-16%29 Factor out the GCF x%5E4


Now let's focus on the inner expression 9x%5E5-16x%5E3%2B9x%5E2-16



9x%5E5-16x%5E3%2B9x%5E2-16 Start with the inner expression

%289x%5E5-16x%5E3%29%2B%289x%5E2-16%29 Group like terms


x%5E3%289x%5E2-16%29%2B1%289x%5E2-16%29 Factor out the GCF x%5E3 out of the first group. Factor out the GCF 1 out of the second group


%28x%5E3%2B1%29%289x%5E2-16%29 Since we have the common term 9x%5E2-16, we can combine like terms




%28x%2B1%29%28x%5E2-x%2B1%29%283x%2B4%29%283x-4%29 Now factor x%5E3%2B1 by using the sum of cubes to get %28x%2B1%29%28x%5E2-x%2B1%29 and factor 9x%5E2-16 by using the difference of squares to get %283x%2B4%29%283x-4%29



x%5E4%28x%2B1%29%28x%5E2-x%2B1%29%283x%2B4%29%283x-4%29 Reintroduce the GCF x%5E4



So 9x%5E9-16x%5E7%2B9x%5E6-16x%5E4 factors to x%5E4%28x%2B1%29%28x%5E2-x%2B1%29%283x%2B4%29%283x-4%29