Question 236687


{{{64m^3+125n^3}}} Start with the given expression.



{{{(4m)^3+(5n)^3}}} Rewrite {{{64m^3}}} as {{{(4m)^3}}}. Rewrite {{{125n^3}}} as {{{(5n)^3}}}.



{{{(4m+5n)((4m)^2-(4m)(5n)+(5n)^2)}}} Now factor by using the sum of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">sum of cubes formula</a> is {{{A^3+B^3=(A+B)(A^2-AB+B^2)}}}



{{{(4m+5n)(16m^2-20mn+25n^2)}}} Multiply


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Answer:


So {{{64m^3+125n^3}}} factors to {{{(4m+5n)(16m^2-20mn+25n^2)}}}.



In other words, {{{64m^3+125n^3=(4m+5n)(16m^2-20mn+25n^2)}}}