Question 549842


{{{8y^3-125}}} Start with the given expression.



{{{(2y)^3-(5)^3}}} Rewrite {{{8y^3}}} as {{{(2y)^3}}}. Rewrite {{{125}}} as {{{(5)^3}}}.



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



{{{(2y-5)(4y^2+10y+25)}}} Multiply


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Answer:

So {{{8y^3-125}}} factors to {{{(2y-5)(4y^2+10y+25)}}}.


In other words, {{{8y^3-125=(2y-5)(4y^2+10y+25)}}}