[tex]\frac{1}{27} x {}^{3} + \frac{27}{64} {y}^{3} = \frac{1}{1728} (64 {x}^{3} + 729y {}^{3} ) = \frac{1}{1728} (4x + 9y)(16 {x}^{2} - 36xy + 81 {y}^{2} )[/tex]

[tex]x {}^{2} - 3x + 3y - y {}^{2} = (x - y)(x + y) + 3y - 3x = (x - y)(x + y) - 3(x - y) = (x - y)(x + y - 3)[/tex]

[tex] {a}^{2} + 4 b {}^{2} - 4ab - ax + 2bx = a {}^{2} - 2 \times a \times 2b + (2b) {}^{2} - x(a - 2b) = (a - 2b) {}^{2} - x(a - 2b) = (a - 2b)(a - 2b - x)[/tex]