Question 202825
{{{3x^6+24}}} Start with the given expression.



{{{3(x^6+8)}}} Factor out the GCF 3



{{{3((x^2)^3+(2)^3)}}} Rewrite {{{x^6}}} as {{{(x^2)^3}}}. Rewrite {{{8}}} as {{{(2)^3}}}.



{{{3(x^2+2)((x^2)^2-(x^2)(2)+(2)^2)}}} Now factor by using the sum of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">sum of cubes formula</a> is {{{A^3+B^3=(A+B)(A^2-AB+B^2)}}}



{{{3(x^2+2)(x^4-2x^2+4)}}} Multiply



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Answer:


So {{{3x^6+24}}} factors to {{{3(x^2+2)(x^4-2x^2+4)}}}.



In other words, {{{3x^6+24=3(x^2+2)(x^4-2x^2+4)}}}