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http://www.purplemath.com/modules/specfact2.htm
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27x^3 - 8y^3
(3*3*3)x^3 - (2*2*2)y^3
3^3x^3 - 2^3y^3
(3x)^3 - (2y)^3
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This is a "special case" of the "difference of two cubes".
a^3 – b^3 = (a – b)(a^2 + ab + b^2)
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Our 'a' = 3x
and 'b' = 2y
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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)
