a) (4x - 3)(x + 2) = 4x(x + 2) - 3(x + 2) = $4x^{2} + 5x - 6$.
b) $(5x +2)(-x^{2} + 3x +1)$ = $5x.(-x^{2} + 3x +1) + 2(-x^{2} + 3x +1)$ = $-5x^{3} + 13x^{2} + 11x + 2$.
c) $(2x^{2}-7x+4)(-3x^{2}+6x+5)\\ = 2x^{2}(-3x^{2}+6x+5) -7x(-3x^{2}+6x+5)+4(-3x^{2}+6x+5)\\ = -6x^{4}+33x^{3}-44x^{2}-11x+20$