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

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 Click here to see ALL problems on Polynomials-and-rational-expressions Question 165067: I need to factor 27x^3 - 8y^3 using the difference of two cubes methodAnswer by nerdybill(6958)   (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)