SOLUTION: I need to factor 27x^3 - 8y^3 using the difference of two cubes method

Question 165067: I need to factor 27x^3 - 8y^3 using the difference of two cubes method
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
This site gives you a better insight:
http://www.purplemath.com/modules/specfact2.htm
.
27x^3 - 8y^3
(3*3*3)x^3 - (2*2*2)y^3
3^3x^3 - 2^3y^3
(3x)^3 - (2y)^3
.
This is a "special case" of the "difference of two cubes".
a^3 � b^3 = (a � b)(a^2 + ab + b^2)
.
Our 'a' = 3x
and 'b' = 2y
.
Therefore:
27x^3 - 8y^3 = (a � b)(a^2 + ab + b^2)
27x^3 - 8y^3 = (3x � 2y)((3x)^2 + (3x)(2y) + (2y)^2)
27x^3 - 8y^3 = (3x � 2y)(9x^2 + 6xy + 4y^2)

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