Question 565162
Let's factor {{{x^3-216}}}



{{{x^3-216}}} Start with the given expression.



{{{(x)^3-(6)^3}}} Rewrite {{{x^3}}} as {{{(x)^3}}}. Rewrite {{{216}}} as {{{(6)^3}}}.



{{{(x-6)((x)^2+(x)(6)+(6)^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)}}}



{{{(x-6)(x^2+6x+36)}}} Multiply



So {{{x^3-216}}} factors to {{{(x-6)(x^2+6x+36)}}}.


In other words, {{{x^3-216=(x-6)(x^2+6x+36)}}}


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So {{{5(x^3-216)}}} becomes {{{5(x-6)(x^2+6x+36)}}}



This means that {{{5x^3-1080}}} fully factors to {{{5(x-6)(x^2+6x+36)}}}



In other words, {{{5x^3-1080=5(x-6)(x^2+6x+36)}}}

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