i) $2ab, -7ab, \ \frac{2}{3} ab, \ 9ab$

$2ab+(-7ab)+\frac{2}{3} ab+9ab$

$=(2-7+\frac{2}{3}+9)ab$

$=\frac{14}{3} ab$

$\\$

ii) $5x^2 y, -3x^2 y,\ \frac{1}{2} x^2 y,\ \frac{4}{5} x^2 y$

$5x^2 y+(-3x^2 y)+\frac{1}{2} x^2 y+\frac{4}{5} x^2 y$

$=(5-3+\frac{1}{2}+\frac{4}{5}) x^2 y$

$=\frac{33}{10} x^2 y$

$\\$

Question 2: Subtract

i) $7xy \ from\ 2xy$

$2xy-7xy=-5xy$

$\\$

ii) $2ab \ from\ -3ab$

$-3ab-2ab= -5ab$

$\\$

iii) $-3a^2 b \ from\ 2a^2 b$

$2a^2 b-(-3a^2 b)=5a^2 b$

$\\$

iv) $-5xy^2 \ from\ -3xy^2$

$-3xy^2-(-5xy^2 )=2xy^2$

$\\$

v) $\frac{(-3)}{7} x^2 y \ from\ \frac{1}{3} x^2 y$

$\frac{1}{3} x^2 y-\frac{(-3)}{7} x^2 y=\frac{16}{21} x^2 y$

$\\$

Question 3: Add the following expression;

i) $3x+8y-5z,\ 7x-9y+6z,\ x -2y-3z,\ -5x+3y+z$

$3x+8y-5z$

$7x-9y+6z$

$x -2y-3z$

$\underline{+ \ \ \ -5x+3y+z}$

$6x \ \ \ \ \ \ -z$

$\\$

ii) $y^2-x^2, 2x^2-3y^2,\ 5y^2-3x^2,\ 6x^2+2y^2$

$y^2-x^2$

$-3y^2+2x^2$

$5y^2-3x^2$

$\underline{+ \ \ \ 2y^2+6x^2}$

$5y^2+4x^2$

$\\$

iii) $2p+3r+4q, 7r+3p-2q,\ q-r-p, \ 5p+4q-8r$

$2p+3r+4q$

$3p+7r-2q$

$-p-r+q$

$\underline{+ \ \ \ 5p-8r+4q}$

$9p+r+7q$

$\\$

iv) $7xy+yz-3zx,\ 2yz+zx-5xy,\ 2zx-3yz+4xy$

$7xy+yz-3zx$

$-5xy+2yz+zx$

$\underline{+ \ \ \ 4xy-3yz+2zx}$

$6xy$

$\\$

v) $1-x-x^2-3x^3,\ 2x^2+x^3+3, \ x^2+5x-2,\ x^3-x^2-3x$

$1-x-x^2-3x^3$

$3 +2x^2+x^3$

$-2-5x+x^2$

$\underline{+ \ \ \ -3x-x^2+x^3}$

$2-9x+x^2-x^3$

$\\$

vi) $4z^4-7z^3+2z-5z^2+3,\ 3z^2+4z^3-2z^4-z-5,\ 3z^3-z-1+z^2$

$4z^4-7z^3-5z^2+2z+3$

$-2z^4+4z^3+3z^2-5$

$\underline{+ \ \ \ +3z^3+z^2-z-1}$

$2z^4-1z^2+z-3$

$\\$

vii) $3+5y-4y^2+7y^3,\ -7+2y+3y^3,\ 5-6y-9y^3+2y^2$

$3+5y-4y^2+7y^3$

$-7+2y+3y^3$

$\underline{+ \ \ \ 5-6y+2y^2-9y^3}$

$3+y-2y^2-y^3$

$\\$

Question 4: Subtract;

(i) $3y-5z \ from\ 6z-4y$

$6z-4y$

$-5z+3y \\ \underline{+ \ \ \ \ \ -\ \ \ \ }$

$11z-7y$

$\\$

(ii) $3a-5b-2c from 2a-3b-c$

$2a -3b-c$

$3a -5b-2c \\ \underline{- \ \ \ \ + \ \ \ \ +\ \ \ \ }$

$-a+2b+c$

$\\$

(iii) $p^2-q^2+5r^2 \ from\ q^2-p^2-2r^2$

$q^2-p^2-2r^2$

$-q^2+p^2+5r^2 \\ \underline{+ \ \ \ - \ \ \ -\ \ \ \ }$

$2q^2-2p^2-7r^2$

$\\$

(iv) $5x^2+x-11 from x^2-2x+8$

$x^2-2x+8$

$5x^2+x-11 \\ \underline{- \ \ \ - \ \ \ + \ \ \ \ }$

$-4x^2-3x+19$

$\\$

(v) $1-x+2x^2-x^3 from 2x^3-x^2+3x+2$

$2x^3-x^2+3x+2$

$-x^3+2x^2-x+ 1 \\ \underline{+ \ \ \ - \ \ \ + \ \ \ -\ \ \ \ }$

$3x^3-3x^2+4x+1$

$\\$

(vi) $7x^3-6x^2 y+9xy^2-2y^3 from 3x^2 y-2x^3+y^3-5xy^2$

$3x^2 y-2x^3+y^3-5xy^2$

$-6x^2 y+7x^3-2y^3+9xy^2 \\ \underline{+ \ \ \ \ \ \ - \ \ \ \ \ \ + \ \ \ \ \ \ -\ \ \ \ }$

$9x^2 y-9x^3+3y^3-14xy^2$

$\\$

Question 5: Subtract the sum of  $4x^2+7xy+3y^2+1$ and $2x^2-5xy-2y^2+8$ from $9x^2-8xy+11y^2$

$4x^2+7xy+3y^2+1$

$\underline{2x^2-5xy-2y^2+8}$

$6x^2+2xy+y^2+9$

Then Subtract

$9x^2-8xy+11y^2$

$6x^2+2xy+y^2+9 \\ \underline{- \ \ \ \ - \ \ \ \ - \ \ \ \ -\ \ \ \ }$

$3x^2-10xy+10y^2-9$

$\\$

Question 6: What must be added to $2x^2+6x-5$ to get $3x^2-2x+6$

$3x^2-2x+6$

$2x^2+6x-5 \\ \underline{- \ \ \ \ \ - \ \ \ \ \ +\ \ \ \ \ }$

$x^2-8x+11$

$\\$

Question 7: What must be added to $4-3x+9x^2$ to get $3-4x^2-x^3$

$3-4x^2-x^3$

$4+9x^2-3x \\ \underline{- \ \ \ \ \ - \ \ \ \ \ +\ \ \ \ \ }$

$-1-13x^2-x^3+3x$

$\\$

Question 8: What must be subtracted from $3x^2 y-2xy^2+7x-2y$ to get $7x^2 y-5x^2 y-3x+3y$

$3x^2 y-2xy^2+7x-2y$

$-5x^2 y+7xy^2-3x+3y \\ \underline{+\ \ \ \ \ - \ \ \ \ \ + \ \ \ \ \ - \ \ \ \ \ }$

$8x^2 y-9xy^2+10x-5y$

$\\$

Question 9: What must be subtract from $a^2+b^2+c^2-3abc$ to get $2a^2-b^2-3c^2+abc$

$a^2+b^2+c^2-3abc$

$2a^2-b^2-3c^2+abc \\ \underline{- \ \ \ \ \ + \ \ \ \ \ + \ \ \ \ \ - \ \ \ \ \ }$

$-a^2+2b^2+4c^2-4abc$

$\\$

Question 10: Subtract $a^3-3a^2$  from $b^3-3b^2$

$b^3-3b^2$

$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a^3- 3a^2 \\ \underline{ - \ \ \ \ \ + \ \ \ \ \ }$

$b^3-3b^2-a^3+3a^2$