Question 200145
{{{9x^4-25x^2}}} Start with the given expression



{{{x^2(9x^2-25)}}} Factor out the GCF {{{x^2}}}



Now let's focus on the inner expression {{{9x^2-25}}}


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{{{9x^2-25}}} Start with the given expression.



{{{(3x)^2-25}}} Rewrite {{{9x^2}}} as {{{(3x)^2}}}.



{{{(3x)^2-(5)^2}}} Rewrite {{{25}}} as {{{(5)^2}}}.



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



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



{{{A^2-B^2=(A+B)(A-B)}}} Start with the difference of squares formula.



{{{(3x)^2-(5)^2=(3x+5)(3x-5)}}} Plug in {{{A=3x}}} and {{{B=5}}}.



So this shows us that {{{9x^2-25}}} factors to {{{(3x+5)(3x-5)}}}.



In other words {{{9x^2-25=(3x+5)(3x-5)}}}.



This means that {{{x^2(9x^2-25)}}} factors further to {{{x^2(3x+5)(3x-5)}}}

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Answer:



So {{{9x^4-25x^2}}} completely factors to {{{x^2(3x+5)(3x-5)}}}



In other words,  {{{9x^4-25x^2=x^2*(3x+5)*(3x-5)}}}