Question 280215


{{{27x^3+1}}} Start with the given expression.



{{{(3x)^3+(1)^3}}} Rewrite {{{27x^3}}} as {{{(3x)^3}}}. Rewrite {{{1}}} as {{{(1)^3}}}.



{{{(3x+1)((3x)^2-(3x)(1)+(1)^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)}}}



{{{(3x+1)(9x^2-3x+1)}}} Multiply


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Answer:


So {{{27x^3+1}}} factors to {{{(3x+1)(9x^2-3x+1)}}}.



In other words, {{{27x^3+1=(3x+1)(9x^2-3x+1)}}}