(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)

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