Question 189581


{{{27x^3-64}}} Start with the given expression.



{{{(3x)^3-(4)^3}}} Rewrite {{{27x^3}}} as {{{(3x)^3}}}. Rewrite {{{64}}} as {{{(4)^3}}}.



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



{{{(3x-4)(9x^2+12x+16)}}} Multiply


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Answer:

So {{{27x^3-64}}} factors to {{{(3x-4)(9x^2+12x+16)}}}.



In other words, {{{27x^3-64=(3x-4)(9x^2+12x+16)}}}