Question 316985


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



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



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



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


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Answer:


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


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