Question 316976


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



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



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



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


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Answer:

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


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