Question 179583


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



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



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



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


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Answer:

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


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