Question 785261


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



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



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



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


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Answer:

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


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