Question 201197


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



{{{(t)^3+(5)^3}}} Rewrite {{{t^3}}} as {{{(t)^3}}}. Rewrite {{{125}}} as {{{(5)^3}}}.



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



{{{(t+5)(t^2-5t+25)}}} Multiply


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Answer:


So {{{t^3+125}}} factors to {{{(t+5)(t^2-5t+25)}}}.


In other words, {{{t^3+125=(t+5)(t^2-5t+25)}}}