Question 323030


{{{27+8t^3}}} Start with the given expression.



{{{(3)^3+(2t)^3}}} Rewrite {{{27}}} as {{{(3)^3}}}. Rewrite {{{8t^3}}} as {{{(2t)^3}}}.



{{{(3+2t)((3)^2-(3)(2t)+(2t)^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)}}}



{{{(3+2t)(9-6t+4t^2)}}} Multiply


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Answer:


So {{{27+8t^3}}} factors to {{{(3+2t)(9-6t+4t^2)}}}.


In other words, {{{27+8t^3=(3+2t)(9-6t+4t^2)}}}