Question 1: Add

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

Answer:

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      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

Answer:

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

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  

Answer:

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}

\\

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

Answer:

(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}

\\

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

Answer:

First Add

\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}

\\

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

Answer:

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

\\

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

Answer:

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

\\

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

Answer:

\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}

\\

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

Answer:

\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}

\\

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

Answer:

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