Question 168971
{{{2x^3-128}}} Start with the given expression



{{{2(x^3-64)}}} Factor out the GCF {{{2}}}



Now let's focus on the inner expression {{{x^3-64}}}



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{{{x^3-64}}} Start with the inner expression.



{{{(x)^3-(4)^3}}} Rewrite {{{x^3}}} as {{{(x)^3}}}. Rewrite {{{64}}} as {{{(4)^3}}}.



{{{(x-4)((x)^2+(x)(4)+(4)^2)}}} Now factor by using the difference of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">difference of cubes formula</a> is {{{A^3-B^3=(A-B)(A^2+AB+B^2)}}}



{{{(x-4)(x^2+4x+16)}}} Multiply



So {{{x^3-64}}} factors to {{{(x-4)(x^2+4x+16)}}}.


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Answer:

So {{{2x^3-128}}} completely factors to {{{2(x-4)(x^2+4x+16)}}}