$6x^3 - 8x^2 + 3xy - 4y = (6x^3 + 3xy) - (8x^2 + 4y) = 3x(2x^2 + y) - 4(2x^2 + y) = (2x^2 + y)(3x - 4)$

$x^4 - 6x^2y + 9y^2 - 16 = (x^4 - 6x^2y + 9y^2) - 4^2 = (x^2 - 3y)^2 - 4^2 = (x^2 - 3y - 4)(x^2 - 3y + 4)$

$\frac{125x^3}{27} - \frac{m^6n^9}{64} = (\frac{5x}{3})^3 - (\frac{m^2n^3}{4})^3 = (\frac{5x}{3} - \frac{m^2n^3}{4})((\frac{5x}{3})^2 + \frac{5x}{3} * \frac{m^2n^3}{4} + (\frac{m^2n^3}{4})^2) = (\frac{5x}{3} - \frac{m^2n^3}{4})(\frac{25x^2}{9} + \frac{5xm^2n^3}{12} + \frac{m^4n^6}{16})$

$c^2 - 2c - b^2 - 4b - 3 = c^2 - 2c - b^2 - 4b - 4 + 1 = (c^2 - 2c + 1) - (b^2 + 4b + 4) = (c - 1)^2 - (b + 2)^2 = (c - 1 - b - 2)(c - 1 + b + 2) = (c - b - 3)(c + b + 1)$.