Question 478688


{{{8x^3+125}}} Start with the given expression.



{{{(2x)^3+(5)^3}}} Rewrite {{{8x^3}}} as {{{(2x)^3}}}. Rewrite {{{125}}} as {{{(5)^3}}}.



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



{{{(2x+5)(4x^2-10x+25)}}} Multiply


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Answer:


So {{{8x^3+125}}} factors to {{{(2x+5)(4x^2-10x+25)}}}.


In other words, {{{8x^3+125=(2x+5)(4x^2-10x+25)}}}