Question 567518


{{{8r^3-27}}} Start with the given expression.



{{{(2r)^3-(3)^3}}} Rewrite {{{8r^3}}} as {{{(2r)^3}}}. Rewrite {{{27}}} as {{{(3)^3}}}.



{{{(2r-3)((2r)^2+(2r)(3)+(3)^2)}}} Now factor by using the difference of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">difference of cubes formula</a> is {{{A^3-B^3=(A-B)(A^2+AB+B^2)}}}



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


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Answer:

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


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