Question 168156
{{{49a^7-9a^5}}} Start with the given expression



{{{a^5(49a^2-9)}}} Factor out the GCF {{{a^5}}}



Now let's focus on the inner expression {{{49a^2-9}}}





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{{{49a^2-9}}} Start with the given expression.



{{{(7a)^2-9}}} Rewrite {{{49a^2}}} as {{{(7a)^2}}}.



{{{(7a)^2-(3)^2}}} Rewrite {{{9}}} as {{{(3)^2}}}.



Notice how we have a difference of squares. So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{(7a+3)(7a-3)}}} Factor the expression using the difference of squares.



So {{{49a^2-9}}} factors to {{{(7a+3)(7a-3)}}}.




So this means that {{{a^5(49a^2-9)}}} factors to {{{a^5(7a+3)(7a-3)}}}.


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Answer:



So {{{49a^7-9a^5}}} completely factors to {{{a^5(7a+3)(7a-3)}}}