合并同类项：
(1)$\frac {1}{4}ab^{2}-5a^{2}b-\frac {3}{4}a^{2}b+0.75ab^{2}$； (2)$\frac {1}{2}x^{2}-3xy^{2}+4y^{2}+\frac {1}{2}x^{2}+5xy^{2}$；
(3)$2x^{2}y-2xy-4xy^{2}+xy+4x^{2}y-3xy^{2}$； (4)$\frac {1}{3}m^{2}n-\frac {1}{2}mn^{2}-nm^{2}+\frac {1}{6}n^{2}m$；
(5)$(-\frac {1}{3}xy)+(-\frac {2}{5}x^{2})-\frac {1}{2}x^{2}-(-\frac {1}{6}xy)$；
(6)$-\frac {1}{5}xy^{2}-3x^{2}y+xy^{2}+2x^{2}y+3xy^{2}+x^{2}y-2xy^{2}$；
(7)$\frac {1}{3}x^{2}y-\frac {1}{2}xy^{2}+\frac {1}{2}xy^{2}+xy-x^{2}y$； (8)$2a^{3}b-\frac {1}{2}a^{3}b-a^{2}b+\frac {1}{2}a^{2}b-ab^{2}$；
(9)$3(n-m)^{2}-7(n-m)+8(n-m)^{2}+6(n-m)$；
(10)$-3(a-3b)^{3}+2(3b-a)^{2}+4(a-3b)^{2}+2(3b-a)^{3}$。
(1)$\frac {1}{4}ab^{2}-5a^{2}b-\frac {3}{4}a^{2}b+0.75ab^{2}$； (2)$\frac {1}{2}x^{2}-3xy^{2}+4y^{2}+\frac {1}{2}x^{2}+5xy^{2}$；
(3)$2x^{2}y-2xy-4xy^{2}+xy+4x^{2}y-3xy^{2}$； (4)$\frac {1}{3}m^{2}n-\frac {1}{2}mn^{2}-nm^{2}+\frac {1}{6}n^{2}m$；
(5)$(-\frac {1}{3}xy)+(-\frac {2}{5}x^{2})-\frac {1}{2}x^{2}-(-\frac {1}{6}xy)$；
(6)$-\frac {1}{5}xy^{2}-3x^{2}y+xy^{2}+2x^{2}y+3xy^{2}+x^{2}y-2xy^{2}$；
(7)$\frac {1}{3}x^{2}y-\frac {1}{2}xy^{2}+\frac {1}{2}xy^{2}+xy-x^{2}y$； (8)$2a^{3}b-\frac {1}{2}a^{3}b-a^{2}b+\frac {1}{2}a^{2}b-ab^{2}$；
(9)$3(n-m)^{2}-7(n-m)+8(n-m)^{2}+6(n-m)$；
(10)$-3(a-3b)^{3}+2(3b-a)^{2}+4(a-3b)^{2}+2(3b-a)^{3}$。
答案：(1)$ab^{2}-\frac {23}{4}a^{2}b$ (2)$x^{2}+2xy^{2}+4y^{2}$ (3)$6x^{2}y-xy-7xy^{2}$ (4)$-\frac {2}{3}m^{2}n-\frac {1}{3}mn^{2}$ (5)$-\frac {1}{6}xy-\frac {9}{10}x^{2}$ (6)$\frac {9}{5}xy^{2}$ (7)$-\frac {2}{3}x^{2}y+xy$ (8)$\frac {3}{2}a^{3}b-\frac {1}{2}a^{2}b-ab^{2}$ (9)$11(n-m)^{2}-(n-m)$ (10)$-5(a-3b)^{3}+6(a-3b)^{2}$
解析：
(1) $\frac{1}{4}ab^{2}-5a^{2}b-\frac{3}{4}a^{2}b+0.75ab^{2}$
$=(\frac{1}{4}ab^{2}+\frac{3}{4}ab^{2})+(-5a^{2}b-\frac{3}{4}a^{2}b)$
$=ab^{2}-\frac{23}{4}a^{2}b$
(2) $\frac{1}{2}x^{2}-3xy^{2}+4y^{2}+\frac{1}{2}x^{2}+5xy^{2}$
$=(\frac{1}{2}x^{2}+\frac{1}{2}x^{2})+(-3xy^{2}+5xy^{2})+4y^{2}$
$=x^{2}+2xy^{2}+4y^{2}$
(3) $2x^{2}y-2xy-4xy^{2}+xy+4x^{2}y-3xy^{2}$
$=(2x^{2}y+4x^{2}y)+(-2xy+xy)+(-4xy^{2}-3xy^{2})$
$=6x^{2}y-xy-7xy^{2}$
(4) $\frac{1}{3}m^{2}n-\frac{1}{2}mn^{2}-nm^{2}+\frac{1}{6}n^{2}m$
$=(\frac{1}{3}m^{2}n-m^{2}n)+(-\frac{1}{2}mn^{2}+\frac{1}{6}mn^{2})$
$=-\frac{2}{3}m^{2}n-\frac{1}{3}mn^{2}$
(5) $(-\frac{1}{3}xy)+(-\frac{2}{5}x^{2})-\frac{1}{2}x^{2}-(-\frac{1}{6}xy)$
$=(-\frac{1}{3}xy+\frac{1}{6}xy)+(-\frac{2}{5}x^{2}-\frac{1}{2}x^{2})$
$=-\frac{1}{6}xy-\frac{9}{10}x^{2}$
(6) $-\frac{1}{5}xy^{2}-3x^{2}y+xy^{2}+2x^{2}y+3xy^{2}+x^{2}y-2xy^{2}$
$=(-\frac{1}{5}xy^{2}+xy^{2}+3xy^{2}-2xy^{2})+(-3x^{2}y+2x^{2}y+x^{2}y)$
$=\frac{9}{5}xy^{2}$
(7) $\frac{1}{3}x^{2}y-\frac{1}{2}xy^{2}+\frac{1}{2}xy^{2}+xy-x^{2}y$
$=(\frac{1}{3}x^{2}y-x^{2}y)+(-\frac{1}{2}xy^{2}+\frac{1}{2}xy^{2})+xy$
$=-\frac{2}{3}x^{2}y+xy$
(8) $2a^{3}b-\frac{1}{2}a^{3}b-a^{2}b+\frac{1}{2}a^{2}b-ab^{2}$
$=(2a^{3}b-\frac{1}{2}a^{3}b)+(-a^{2}b+\frac{1}{2}a^{2}b)-ab^{2}$
$=\frac{3}{2}a^{3}b-\frac{1}{2}a^{2}b-ab^{2}$
(9) $3(n-m)^{2}-7(n-m)+8(n-m)^{2}+6(n-m)$
$=(3(n-m)^{2}+8(n-m)^{2})+(-7(n-m)+6(n-m))$
$=11(n-m)^{2}-(n-m)$
(10) $-3(a-3b)^{3}+2(3b-a)^{2}+4(a-3b)^{2}+2(3b-a)^{3}$
$=-3(a-3b)^{3}-2(a-3b)^{3}+2(a-3b)^{2}+4(a-3b)^{2}$
$=-5(a-3b)^{3}+6(a-3b)^{2}$
$=(\frac{1}{4}ab^{2}+\frac{3}{4}ab^{2})+(-5a^{2}b-\frac{3}{4}a^{2}b)$
$=ab^{2}-\frac{23}{4}a^{2}b$
(2) $\frac{1}{2}x^{2}-3xy^{2}+4y^{2}+\frac{1}{2}x^{2}+5xy^{2}$
$=(\frac{1}{2}x^{2}+\frac{1}{2}x^{2})+(-3xy^{2}+5xy^{2})+4y^{2}$
$=x^{2}+2xy^{2}+4y^{2}$
(3) $2x^{2}y-2xy-4xy^{2}+xy+4x^{2}y-3xy^{2}$
$=(2x^{2}y+4x^{2}y)+(-2xy+xy)+(-4xy^{2}-3xy^{2})$
$=6x^{2}y-xy-7xy^{2}$
(4) $\frac{1}{3}m^{2}n-\frac{1}{2}mn^{2}-nm^{2}+\frac{1}{6}n^{2}m$
$=(\frac{1}{3}m^{2}n-m^{2}n)+(-\frac{1}{2}mn^{2}+\frac{1}{6}mn^{2})$
$=-\frac{2}{3}m^{2}n-\frac{1}{3}mn^{2}$
(5) $(-\frac{1}{3}xy)+(-\frac{2}{5}x^{2})-\frac{1}{2}x^{2}-(-\frac{1}{6}xy)$
$=(-\frac{1}{3}xy+\frac{1}{6}xy)+(-\frac{2}{5}x^{2}-\frac{1}{2}x^{2})$
$=-\frac{1}{6}xy-\frac{9}{10}x^{2}$
(6) $-\frac{1}{5}xy^{2}-3x^{2}y+xy^{2}+2x^{2}y+3xy^{2}+x^{2}y-2xy^{2}$
$=(-\frac{1}{5}xy^{2}+xy^{2}+3xy^{2}-2xy^{2})+(-3x^{2}y+2x^{2}y+x^{2}y)$
$=\frac{9}{5}xy^{2}$
(7) $\frac{1}{3}x^{2}y-\frac{1}{2}xy^{2}+\frac{1}{2}xy^{2}+xy-x^{2}y$
$=(\frac{1}{3}x^{2}y-x^{2}y)+(-\frac{1}{2}xy^{2}+\frac{1}{2}xy^{2})+xy$
$=-\frac{2}{3}x^{2}y+xy$
(8) $2a^{3}b-\frac{1}{2}a^{3}b-a^{2}b+\frac{1}{2}a^{2}b-ab^{2}$
$=(2a^{3}b-\frac{1}{2}a^{3}b)+(-a^{2}b+\frac{1}{2}a^{2}b)-ab^{2}$
$=\frac{3}{2}a^{3}b-\frac{1}{2}a^{2}b-ab^{2}$
(9) $3(n-m)^{2}-7(n-m)+8(n-m)^{2}+6(n-m)$
$=(3(n-m)^{2}+8(n-m)^{2})+(-7(n-m)+6(n-m))$
$=11(n-m)^{2}-(n-m)$
(10) $-3(a-3b)^{3}+2(3b-a)^{2}+4(a-3b)^{2}+2(3b-a)^{3}$
$=-3(a-3b)^{3}-2(a-3b)^{3}+2(a-3b)^{2}+4(a-3b)^{2}$
$=-5(a-3b)^{3}+6(a-3b)^{2}$