If 9x2 + 6xy + 4y2 is a factor of 27x3 - 8y3, find the other factor.

If 9x2 + 6xy + 4y2 is a factor of 27x3 - 8y3, find the other factor.

Answer Details

27x3 - 8y3 = (3x - 2y)3
But 9x2 + 6xy + 4y2 = (3x +2y)2
So, 27x3 - 8y3 = (3x - 2y)(3x - 2y)2
Hence the other factor is 3x - 2y