Question 636373


{{{8y^3+27x^3}}} Start with the given expression.



{{{(2y)^3+(3x)^3}}} Rewrite {{{8y^3}}} as {{{(2y)^3}}}. Rewrite {{{27x^3}}} as {{{(3x)^3}}}.



{{{(2y+3x)((2y)^2-(2y)(3x)+(3x)^2)}}} Now factor by using the sum of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">sum of cubes formula</a> is {{{A^3+B^3=(A+B)(A^2-AB+B^2)}}}



{{{(2y+3x)(4y^2-6xy+9x^2)}}} Multiply


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Answer:


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


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