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

 `a)``3x(12x-4)-9x(4x-3)`

`=36x^2-12x-36x^2+27x`

`=(36x^2-36x^2)+(-12x+27x)`

`=15x`

`b)x(5-2x)+2x(x-1)`

`=5x-2x^2+2x^2-2x`

`=(5x-2x)+(-2x^2+2x^2)`

`=3x`

`c)(x^2-2xy-3)(x-y)`

`=x^3-x^2y-2x^2y+2xy^2-3x+3y`

`=x^3+(-x^2y-2x^2y)+2xy^2-3x+3y`

`=x^3-3x^2y+2xy^2-3x+3y`

`d)x(2x^2-3)-x^2(5x+1)+x^2`

`=2x^3-3x-5x^3-x^2+x^2`

`=(2x^3-5x^3)-3x+(-x^2+x^2)`

`=-3x^3-3x`

`e)(x-1)(x^2+x+1)`

`=x^3+x^2+x-x^2-x-1`

`=x^3+(x^2-x^2)+(x-x)-1`

`=x^3-1`

`f)(x^3+x^2y+xy^2+y^3)(x-y)`

`=x^4-x^3y+x^3y-x^2y^2+x^2y^2-xy^3+xy^3-y^4`

`=x^4+(-x^3y+x^3y)+(-x^2y^2+x^2y^3)+(-xy^3+xy^3)-y^4`

`=x^4-y^4`