Question 154219


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



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



{{{(5x+4)((5x)^2-(5x)(4)+(4)^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)}}}



{{{(5x+4)(25x^2-20x+16)}}} Multiply


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Answer:


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


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