i) $2ab, -7ab,$ $\frac{2}{3}$ $ab, 9ab$          ii) $5x^2 y, -3x^2 y,$ $\frac{1}{2}$ $x^2 y,$ $\frac{4}{5}$ $x^2 y$

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

$5x^2 y+(-3x^2 y)+$ $\frac{1}{2}$ $x^2 y+$ $\frac{4}{5}$ $x^2 y$ $=(5-3+\frac{1}{2}+$ $\frac{4}{5}$ $) x^2 y =$ $\frac{33}{10}$ $x^2 y$

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Question 2: Subtract:

i) $7xy$ from $2xy$     ii) $2ab$ from $-3ab$

iii) $-3a^2 b$ from $2a^2 b$     iv) $-5xy^2$ from $-3xy^2$

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

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

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Question 3: Add the following expression:

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

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

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

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

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

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

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

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

$\begin{array}{r r} & 3x+8y-5z \\ & 7x-9y+6z \\ & x -2y-3z \\ (+) & -5x+3y+z \\ \hline & {6x \hspace{1.0cm} -z} \end{array}$

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

$\begin{array}{r r} & y^2-x^2 \\ & -3y^2+2x^2 \\ & 5y^2-3x^2 \\ (+) & 2y^2+6x^2 \\ \hline & 5y^2+4x^2 \end{array}$

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

$\begin{array}{r r} & 2p+3r+4q \\ & 3p+7r-2q \\ & -p-r+q \\ (+) & 5p-8r+4q \\ \hline & 9p+r+7q \end{array}$

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

$\begin{array}{r r} & 7xy+yz-3zx \\ & -5xy+2yz+zx \\ (+) & 4xy-3yz+2zx \\ \hline & 6xy \end{array}$

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

$\begin{array}{r r} & 1-x-x^2-3x^3 \\ & 3 +2x^2+x^3 \\ & -2-5x+x^2 \\ (+) & -3x-x^2+x^3 \\ \hline & 2-9x+x^2-x^3 \end{array}$

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

$\begin{array}{r r} & 4z^4-7z^3-5z^2+2z+3 \\ & -2z^4+4z^3+3z^2-5 \\ (+) & +3z^3+z^2-z-1 \\ \hline & 2z^4-1z^2+z-3 \end{array}$

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

$\begin{array}{r r} & 3+5y-4y^2+7y^3 \\ & -7+2y+3y^3 \\ (+) & 5-6y+2y^2-9y^3 \\ \hline & 3+y-2y^2-y^3 \end{array}$

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Question 4: Subtract:

(i) $3y-5z$ form $6z-4y$

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

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

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

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

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

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

$\begin{array}{rr} & 6z-4y \\ (-) & -5z+3y \\ \hline & 11z-7y \end{array}$

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

$\begin{array}{rr} & 2a -3b-c \\ (-) & 3a -5b-2c \\ \hline & -a+2b+c \end{array}$

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

$\begin{array}{rr} & q^2-p^2-2r^2 \\ (-) & -q^2+p^2+5r^2 \\ \hline & 2q^2-2p^2-7r^2 \end{array}$

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

$\begin{array}{rr} & x^2-2x+8 \\ (-) & 5x^2+x-11 \\ \hline & -4x^2-3x+19\end{array}$

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

$\begin{array}{rr} & 2x^3-x^2+3x+2 \\ (-) & -x^3+2x^2-x+ 1 \\ \hline & 3x^3-3x^2+4x+1 \end{array}$

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

$\begin{array}{rr} & 3x^2 y-2x^3+y^3-5xy^2 \\ (-) & -6x^2 y+7x^3-2y^3+9xy^2 \\ \hline & 9x^2 y-9x^3+3y^3-14xy^2 \end{array}$

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

$\begin{array}{r r} & 4x^2+7xy+3y^2+1 \\ (+) & 2x^2-5xy-2y^2+8 \\ \hline & 6x^2+2xy+y^2+9 \end{array}$

Then Subtract

$\begin{array}{rr} & 9x^2-8xy+11y^2 \\ (-) & 6x^2+2xy+y^2+9 \\ \hline & 3x^2-10xy+10y^2-9 \end{array}$

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

$\begin{array}{rr} & 3x^2-2x+6 \\ (-) & 2x^2+6x-5 \\ \hline & x^2-8x+11 \end{array}$

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

$\begin{array}{rr} & 3-4x^2-x^3 \\ (-) & 4+9x^2-3x \\ \hline & -1-13x^2-x^3+3x \end{array}$

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

$\begin{array}{rr} & 3x^2 y-2xy^2+7x-2y \\ (-) & 7x y^2-5x^2 y-3x+3y \\ \hline & -9xy^2+8x^2 y+10x-5y \end{array}$

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

$\begin{array}{rr} & a^2+b^2+c^2-3abc \\ (-) & 2a^2-b^2-3c^2+abc \\ \hline & -a^2 + 2b^2 + 4c^2 - 4abc \end{array}$
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Question 10: Subtract $a^3-3a^2$  from $b^3-3b^2$
$\begin{array}{rr} & b^3-3b^2 \\ (-) & a^3-3a^2 \\ \hline & b^3-3b^2-a^3+3a^2 \end{array}$