Subtract:
(i) − 5xy from 12xy
(ii) 2a2 from − 7a2
(iii) 2a − b from 3a − 5b
(iv) 2x3 − 4x2 + 3x + 5 from 4x3 + x2 + x + 6
(v) $\frac{2}{3} y^{3}-\frac{2}{7} y^{2}-5$ from $\frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2$
(vi) $\frac{3}{2} x-\frac{5}{4} y-\frac{7}{2} z$ from $\frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z$
(vii) $x^{2} y-\frac{4}{5} x y^{2}+\frac{4}{3} x y$ from $\frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}-\frac{1}{3} x y$
(viii) $\frac{a b}{7}-\frac{35}{3} b c+\frac{6}{5} a c$ from $\frac{3}{5} b c-\frac{4}{5} a c$
(i) $12 x y-(-5 x y)$
$=12 x y+5 x y$
$=17 x y$
(ii) $-7 a^{2}-\left(2 a^{2}\right)$
$=-7 a^{2}-2 a^{2}$
$=-9 a^{2}$
(iii) $(3 a-5 b)-(2 a-b)$
$=(3 a-5 b)-2 a+b$
$=3 a-5 b-2 a+b$
$=3 a-2 a-5 b+b$
$=a-4 b$
(iv) $\left(4 x^{3}+x^{2}+x+6\right)-\left(2 x^{3}-4 x^{2}+3 x+5\right)$
$=4 x^{3}+x^{2}+x+6-2 x^{3}+4 x^{2}-3 x-5$
$=4 x^{3}-2 x^{3}+x^{2}+4 x^{2}+x-3 x+6-5 \quad$ (Collecting like terms)
$=2 x^{3}+5 x^{2}-2 x+1 \quad$ (Combining like terms)
(v) $\left(\frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2\right)-\left(\frac{2}{3} y^{3}-\frac{2}{7} y^{2}-5\right)$
$=\frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2-\frac{2}{3} y^{3}+\frac{2}{7} y^{2}+5$
$=\frac{1}{3} y^{3}-\frac{2}{3} y^{3}+\frac{5}{7} y^{2}+\frac{2}{7} y^{2}+y-2+5$ (Collecting like terms)
$=-\frac{1}{3} y^{3}+y^{2}+y+3$ (Collecting like terms)
(vi) $\left(\frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z\right)-\left(\frac{3}{2} x-\frac{5}{4} y-\frac{7}{2} z\right)$
$=\frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z-\frac{3}{2} x+\frac{5}{4} y+\frac{7}{2} z$
$=\frac{2}{3} x-\frac{3}{2} x+\frac{3}{2} y+\frac{5}{4} y-\frac{4}{3} z+\frac{7}{2} z$ (Collecting like terms)
$=-\frac{5}{6} x+\frac{11}{4} y+\frac{13}{6} z$ (Collecting like terms)
(vii) $\left(\frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}-\frac{1}{3} x y\right)-\left(x^{2} y-\frac{4}{5} x y^{2}+\frac{4}{3} x y\right)$
$=\frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}-\frac{1}{3} x y-x^{2} y+\frac{4}{5} x y^{2}-\frac{4}{3} x y$
$=\frac{2}{3} x^{2} y-x^{2} y+\frac{3}{2} x y^{2}+\frac{4}{5} x y^{2}-\frac{1}{3} x y-\frac{4}{3} x y$ (Collecting like terms)
$=-\frac{1}{3} x^{2} y+\frac{23}{10} x y^{2}-\frac{5}{3} x y$ (Collecting like terms)
(viii) $\left(\frac{3}{5} b c-\frac{4}{5} a c\right)-\left(\frac{a b}{7}-\frac{35}{3} b c+\frac{6}{5} a c\right)$
$=\frac{3}{5} b c-\frac{4}{5} a c-\frac{a b}{7}+\frac{35}{3} b c-\frac{6}{5} a c$
$=\frac{3}{5} b c+\frac{35}{3} b c-\frac{4}{5} a c-\frac{6}{5} a c-\frac{a b}{7}$ (Combining like terms)
$=\frac{184}{15} b c-2 a c-\frac{a b}{7}$ (Combining like terms)