Question 607182


{{{27y^3-125x^3}}} Start with the given expression.



{{{(3y)^3-(5x)^3}}} Rewrite {{{27y^3}}} as {{{(3y)^3}}}. Rewrite {{{125x^3}}} as {{{(5x)^3}}}.



{{{(3y-5x)((3y)^2+(3y)(5x)+(5x)^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)}}}



{{{(3y-5x)(9y^2+15xy+25x^2)}}} Multiply


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Answer:

So {{{27y^3-125x^3}}} factors to {{{(3y-5x)(9y^2+15xy+25x^2)}}}.


In other words, {{{27y^3-125x^3=(3y-5x)(9y^2+15xy+25x^2)}}}

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