Question 119395
{{{9x^9-16x^7+9x^6-16x^4}}} Start with the given expression



{{{x^4(9x^5-16x^3+9x^2-16)}}} Factor out the GCF {{{x^4}}}



Now let's focus on the inner expression {{{9x^5-16x^3+9x^2-16}}}




{{{9x^5-16x^3+9x^2-16}}} Start with the inner expression


{{{(9x^5-16x^3)+(9x^2-16)}}} Group like terms



{{{x^3(9x^2-16)+1(9x^2-16)}}} Factor out the GCF {{{x^3}}} out of the first group. Factor out the GCF {{{1}}} out of the second group



{{{(x^3+1)(9x^2-16)}}} Since we have the common term {{{9x^2-16}}}, we can combine like terms





{{{(x+1)(x^2-x+1)(3x+4)(3x-4)}}} Now factor {{{x^3+1}}} by using the sum of cubes to get {{{(x+1)(x^2-x+1)}}} and factor {{{9x^2-16}}} by using the difference of squares to get {{{(3x+4)(3x-4)}}}




{{{x^4(x+1)(x^2-x+1)(3x+4)(3x-4)}}} Reintroduce the GCF {{{x^4}}}




So {{{9x^9-16x^7+9x^6-16x^4}}} factors to {{{x^4(x+1)(x^2-x+1)(3x+4)(3x-4)}}}