How do I factor 64x^3-27y^12
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This also looks like the difference of two cubes (a3 - b3) = (a - b) (a2 + ab + b2), since
64 = 43 and 27 = 33. Also, y12 = (y4)3 So,
64x3 - 27y12 = (4x)3 - (3y4)3
(4x - 3y4)[(4x)2 + (4x)(3y4) + (3y4)2]
(4x - 3y4)[16x2 + 12xy4 + 9y8]