a) $(-4x^{3}-13x^{2}+2x^{5})+(13x^{2}+2x^{3}-12x-1)$
= $-4x^{3}-13x^{2}+2x^{5}+13x^{2}+2x^{3}-12x-1=2x^{5}-2x^{3}-12x-1$
b) $(12x^{6}-11x^{2}+3x^{3}+9)-(13x^{6}+2x^{3}-11x^{2}-11x)$
= $12x^{6}-11x^{2}+3x^{3}+9-13x^{6}-2x^{3}+11x^{2}+11x=-x^{6}+x^{3}+11x+9$
c) $(8x^{3}-x^{2}+1)(x^{2}-1)=8x^{5}-8x^{3}-x^{4}+x^{2}+x^{2}-1=8x^{5}-8x^{3}-x^{4}+2x^{2}-1$
d) $(8x^{3}+6x^{2}+3x+1)/(2x+1)=4x^{2}+x+1$