Bài giải:

A + B = $\left( 2{{x}^{3}}-4{{x}^{2}}y+1\frac{1}{3}.x{{y}^{2}}-{{y}^{4}}+1 \right)+\left( -2{{x}^{3}}-1\frac{1}{2}.{{x}^{2}}y+\frac{2}{3}x{{y}^{2}}-{{y}^{4}}-3 \right)$

= $2{{x}^{3}}-4{{x}^{2}}y+1\frac{1}{3}x{{y}^{2}}-{{y}^{4}}+1-2{{x}^{3}}-1\frac{1}{2}{{x}^{2}}y+\frac{2}{3}x{{y}^{2}}-{{y}^{4}}-3$

= $2{{x}^{3}}-4{{x}^{2}}y+\frac{4}{3}x{{y}^{2}}-{{y}^{4}}+1-2{{x}^{3}}-\frac{3}{2}{{x}^{2}}y+\frac{2}{3}x{{y}^{2}}-{{y}^{4}}-3$

= $(2{{x}^{3}}-2{{x}^{3}})+\left( -4{{x}^{2}}y-\frac{3}{2}{{x}^{2}}y \right)+\left( \frac{4}{3}x{{y}^{2}}+\frac{2}{3}x{{y}^{2}} \right)+(-{{y}^{4}}-{{y}^{4}})+(1-3)$

= $4{{x}^{3}}-\frac{5}{2}{{x}^{2}}y+2x{{y}^{2}}-2{{y}^{4}}+2$

Đáp án đúng là: A