`1)`

`a) 2/3 x^3 . (1/4 x^2 + 3x - 5)`

`= 2/3 x^3 . 1/4 x^2 + 2/3 . x^3 + 3x - 2/3 x^3 - 5`

`= `1/6 x^5 + 3x - 5`

`b) (3a^2 - 1/2 a + 5) . 2a`

`= 3a^2 . 2a - 1/2 a . 2a + 5 . 2a`

`= 6a^3 - a^5 + 10a`

`2)`

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

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

`= 2x^3 - 6x + 5x^2 - 15`

`b) (x + 2)(x^2 - 2x + 4)`

`= x . x^2 - x . 2x + 4x + 2x^2 - 2 . 2x + 2 . 4`

`= x^3 - 2x^2 + 4x + 2x^2 - 4x + 8`

`= x^3 +8`

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

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

`= x^3 - 10x^2 - 2x^2 + 10x + 3x - 15`

`= x^3 - 12x^2 + 13x - 15`