2. a, (x²y + 3x²y) + (-3xy + xy + 5xy) + (-1/2x - 8/5x) - 7 b, (5xy² + 1/2 xy²) + (3xy + xy + 6xy) - (1/3x + 2/3) + (1/2 - 1/4) c, C= 8x³y - 2x²y² + 1/2x + 8 - 3x³y + x²y² - 1/4x - 9 + 5xy - 1/2x + xy - 7 d, D= 5xy - 8x²y - xy - 5/2y + 7 - 5/4y - 8xy - 3x²y - 7x- 8 - 1/2y + 9

$a,$ $\left(x^2y+3x^2y\right)+\left(-3xy+xy+5xy\right)+\left(-\dfrac{1}{2}x-\dfrac{8}{5}x\right)-7$

$=x^2y+3x^2y-3xy+xy+5xy-\dfrac{1}{2}x-\dfrac{8}{5}x-7$

$=4x^2y-3xy+xy+5xy-\dfrac{1}{2}x-\dfrac{8}{5}x-7$

$=4x^2y+3xy-\dfrac{1}{2}x-\dfrac{8}{5}x-7$

$=4x^2y+3xy+x\left(-\dfrac{1}{2}-\dfrac{8}{5}\right)-7$

$=4x^2y+3xy-\dfrac{21}{10}x-7$

$b,$ $\left(5xy^2+\dfrac{1}{2}xy^2\right)+\left(3xy+xy+6xy\right)-\left(\dfrac{1}{3}x+\dfrac{2}{3}\right)+\left(\dfrac{1}{2}-\dfrac{1}{4}\right)$

$=5xy^2+\dfrac{1}{2}xy^2+3xy+xy+6xy-\left(\dfrac{1}{3}x+\dfrac{2}{3}\right)+\dfrac{1}{2}-\dfrac{1}{4}$

$=5xy^2+\dfrac{1}{2}xy^2+10xy-\left(\dfrac{1}{3}x+\dfrac{2}{3}\right)+\dfrac{1}{2}-\dfrac{1}{4}$

$=xy^2\left(5+\dfrac{1}{2}\right)+10xy-\left(\dfrac{1}{3}x+\dfrac{2}{3}\right)+\dfrac{1}{2}-\dfrac{1}{4}$

$=xy^2\dfrac{11}{2}+10xy-\dfrac{x}{3}-\dfrac{2}{3}+\dfrac{1}{2}-\dfrac{1}{4}$

$=\dfrac{11}{2}xy^2+10xy-\dfrac{x}{3}-\dfrac{5}{12}$

$=\dfrac{11xy^2}{2}+10xy-\dfrac{x}{3}-\dfrac{5}{12}$

$c,$ $C=8x^3y-2x^2y^2+\dfrac{1}{2}x+8-3x^3y+x^2y^2-\dfrac{1}{4}x-9+5xy-\dfrac{1}{2}x+xy-7$

$=\dfrac{1}{2}x-\dfrac{1}{2}x+8x^3y-3x^3y-2x^2y^2+x^2y^2-\dfrac{1}{4}x+5xy+xy+8-9-7$

$=8x^3y-3x^3y-2x^2y^2+x^2y^2-\dfrac{1}{4}x+5xy+xy+8-9-7$

$=8x^3y-3x^3y-2x^2y^2+x^2y^2-\dfrac{1}{4}x+5xy+xy-8$

$=5x^3y-2x^2y^2+x^2y^2-\dfrac{1}{4}x+5xy+xy-8$

$=5x^3y-x^2y^2-\dfrac{1}{4}x+5xy+xy-8$

$=5x^3y-x^2y^2-\dfrac{1}{4}x+6xy-8$

$d,$ $D=5xy-8x^2y-xy-\dfrac{5}{2}y+7-\dfrac{5}{4}y-8xy-3x^2y-7x-8-\dfrac{1}{2}y+9$

$=5xy-xy-8xy-\frac{5}{2}y-\dfrac{5}{4}y-\dfrac{1}{2}y-8x^2y-3x^2y-7x+8$

$=-4xy-\dfrac{5}{2}y-\dfrac{5}{4}y-\dfrac{1}{2}y-8x^2y-3x^2y-7x+8$

$=-4xy-\dfrac{5}{2}y-\dfrac{5}{4}y-\dfrac{1}{2}y-11x^2y-7x+8$

$=-4xy+y\left(-\dfrac{5}{2}-\dfrac{5}{4}-\dfrac{1}{2}\right)-11x^2y-7x+8$

$=-4xy-\dfrac{17}{4}y-11x^2y-7x+8$