a) 3x(12x - 4) - 9x(4x - 3)
= 3x.12x - 3x.4 - 9x.4x + 9x.3
= 36x² - 12x - 36x² + 27x
= 15x
b) x(5 - 2x) + 2x(x - 1)
= x.5 - x.2x + 2x.x - 2x.1
= 5x - 2x² + 2x² - 2x
= 3x
c) (x² - 2xy - 3)(x - y)
= x².x - 2xy.x - 3.x - x².y + 2xy.y + 3.y
= x³ - 2x²y - 3x - x²y + 2xy² + 3y
= x³ - 3x²y + 2xy² - 3x + 3y
d) x(2x² - 3) - x²(5x + 1) + x²
= x.2x² - x.3 - x².5x - x².1 + x²
= 2x³ - 3x - 5x³ - x² + x²
= -3x³ - 3x
e) (x - 1)(x² + x + 1)
= x.x² + x.x + x.1 - 1.x² - 1.x - 1.1
= x³ + x² + x - x² - x - 1
= x³ - 1
f) (x³ + x²y + xy² + y³) (x - y)
= x³.x + x²y.x + xy².x + y³.x - x³.y - x²y.y - xy².y - y³.y
= x⁴ + x³y + x²y² + xy³ - x³y - x²y² - xy³ - y⁴
= x⁴ - y⁴
