Question 150911
Do you want to factor?


{{{x^3y^6-64}}} Start with the given expression.



{{{(xy^2)^3-(4)^3}}} Rewrite {{{x^3y^6}}} as {{{(xy^2)^3}}}. Rewrite {{{64}}} as {{{(4)^3}}}.



{{{(xy^2-4)((xy^2)^2+(xy^2)(4)+(4)^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)}}}



{{{(xy^2-4)(x^2y^4+4xy^2+16)}}} Multiply


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Answer:

So {{{x^3y^6-64}}} factors to {{{(xy^2-4)(x^2y^4+4xy^2+16)}}}.


In other words, {{{x^3y^6-64=(xy^2-4)(x^2y^4+4xy^2+16)}}}