Question 629844


{{{x^3-512}}} Start with the given expression.



{{{(x)^3-(8)^3}}} Rewrite {{{x^3}}} as {{{(x)^3}}}. Rewrite {{{512}}} as {{{(8)^3}}}.



{{{(x-8)((x)^2+(x)(8)+(8)^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-8)(x^2+8x+64)}}} Multiply


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Answer:

So {{{x^3-512}}} factors to {{{(x-8)(x^2+8x+64)}}}.


In other words, {{{x^3-512=(x-8)(x^2+8x+64)}}}


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