Subtract:
(i) $-5xy$ from $12xy$
(ii) $2a^2$ from $-7a^2$
(iii) $ 2 a-b $ from $ 3 a-5 b $
(iv) $ 2 x^{3}-4 x^{2}+3 x+5 $ from $ 4 x^{3}+x^{2}+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 $
To do:
We have to subtract the given algebraic expressions.
Solution:
(i) $12 x y-(-5 x y)=12 x y+5 x y$
$=17 x y$
(ii) $-7 a^{2}-2 a^{2}=(-7-2)a^2$
$=-9 a^{2}$
(iii) $(3 a-5 b)-(2 a-b)=3 a-5 b-2 a+b$
$=3 a-2 a-5 b+b$
$=a-4 b$
(iv) $(4 x^{3}+x^{2}+x+6)-(2 x^{3}-4 x^{2}+3 x+5)=4 x^{3}+x^{2}+x+6-2 x^{3}+4 x^{2}-3 x-5$
$=4 x^{3}-2 x^{3}+x^{2}+4 x^{2}+x-3 x+6-5$
$=2 x^{3}+5 x^{2}-2 x+1$
(v) $(\frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2)-(\frac{2}{3} y^{3}-\frac{2}{7} y^{2}-5)$
$=\frac{1}{3} y^{3}+\frac{5}{7} y^{2}+y-2-\frac{2}{3} y^{3}+\frac{2}{7} y^{2}+5$
$=\frac{1}{3} y^{3}-\frac{2}{3} y^{3}+\frac{5}{7} y^{2}+\frac{2}{7} y^{2}+y-2+5$
$=\frac{1-2}{3} y^{3}+\frac{5+2}{7} y^{2}+y+3$
$=\frac{-1}{3} y^{3}+\frac{7}{7} y^{2}+y+3$
$=\frac{-1}{3} y^{3}+y^{2}+y+3$
(vi) $(\frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z)-(\frac{3}{2} x-\frac{5}{4} y-\frac{7}{2} z)=\frac{2}{3} x+\frac{3}{2} y-\frac{4}{3} z-\frac{3}{2} x+\frac{5}{4} y+\frac{7}{2} z$
$=\frac{2}{3} x-\frac{3}{2} x+\frac{3}{2} y+\frac{5}{4} y-\frac{4}{3} z+\frac{7}{2} z$
$=\frac{4-9}{6} x+\frac{6+5}{4} y+\frac{-8+21}{6} z$
$=\frac{-5}{6} x+\frac{11}{4} y+\frac{13}{6} z$
(vii) $(\frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}-\frac{1}{3} x y)=\frac{2}{3} x^{2} y+\frac{3}{2} x y^{2}-\frac{1}{3} x y-x^{2} y+\frac{4}{5} x y^{2}-\frac{4}{3} x y$
$=\frac{2}{3} x^{2} y-x^{2} y+\frac{3}{2} x y^{2}+\frac{4}{5} x y^{2}-\frac{1}{3} x y-\frac{4}{3} x y$
$=(\frac{2}{3}-1) x^{2} y+(-\frac{3}{2}+\frac{4}{5}) x y^{2}+(\frac{-1}{3}-\frac{4}{3}) x y$
$=\frac{2-3}{3} x^{2} y+\frac{15+8}{10} x y^{2}+\frac{-1-4}{3} x y$
$=\frac{23}{10} x y^{2}-\frac{5}{3} x y$
(viii) $(\frac{3}{5} b c-\frac{4}{5} a c)-(\frac{a b}{7}-\frac{35}{3} b c+\frac{6}{5} a c)$
$=\frac{3}{5} b c-\frac{4}{5} a c-\frac{1}{7} a b+\frac{35}{3} b c-\frac{6}{5} a c$
$=\frac{3}{5} b c+\frac{35}{3} b c-\frac{4}{5} a c-\frac{6}{5} a c-\frac{1}{7} a b$
$=(\frac{3}{5}+\frac{35}{3}) b c+(\frac{-4}{5}-\frac{6}{5}) a c-\frac{1}{7} a b$
$=\frac{9+175}{15} b c+\frac{-4-6}{5} a c-\frac{1}{7} a b$
$=\frac{184}{15} b c-\frac{10}{5} a c-\frac{1}{7} a b$
$=-\frac{1}{7} a b-2 a c+\frac{184}{15} b c$
$=\frac{1}{7} a b+\frac{184}{15} b c-2 a c$
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