Question 1094764
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<pre>
= {{{m*(64m^3 - 27n^3)}}} = {{{m*((4m)^3-(3n)^3)}}} = {{{m*(4m - 3n)*((4m)^2 + (4m)*(3n) + (3n)^2)}}},

and you may simplify it further, if you want.


The basic identity is  {{{a^3 - b^3)}}} = {{{(a-b)*(a^2 + ab + b^2)}}},


which you must memorize.
</pre>


1. The <B>cube of the sum formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{(a + b)^3 = a^3 + 3a^2*b + 3a*b^2 + b^3}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-cube-of-a-sum-formula.lesson>The cube of the sum formula</A> in this site.



2. The <B>cube of the difference formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;{{{(a - b)^3 = a^3 - 3a^2*b + 3a*b^2 - b^3}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-cube-of-a-difference.lesson>The cube of the difference formula</A>  in this site.



3. The <B>sum of cubes formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{a^3 + b^3 = (a + b)*(a^2 - ab + b^2)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-sum-of-cubes-formula.lesson>The sum of cubes formula</A> in this site.


4. The <B>difference of cubes formula</B> is &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{a^3 - b^3 = (a - b)*(a^2 + ab + b^2)}}}.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;For details and examples of applications of this formula see the lesson <A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/The-difference-of-cubes-formula.lesson>The difference of cubes formula</A>  in this site.