Q1. Add

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

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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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Q2. Subtractm3x

i) 7xy \ from\  2xy

2xy-7xy=-5xy

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ii) 2ab \ from\ -3ab

-3ab-2ab= -5ab

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iii) -3a^2 b \ from\  2a^2 b

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

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iv) -5xy^2 \ from\  -3xy^2

 -3xy^2-(-5xy^2 )=2xy^2

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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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Q.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 

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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

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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

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

7xy+yz-3zx

-5xy+2yz+zx

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

6xy

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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 m54x

3      +2x^2+x^3

-2-5x+x^2

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

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

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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

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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

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Q.4 Subtract;

3y-5z \ from\  6z-4y

6z-4y

-5z+3y

\underline{+   \ \ \ \ \  -\ \ \ \ }

11z-7y

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3a-5b-2c from 2a-3b-c

2a  -3b-c

3a -5b-2c

\underline{- \ \ \ \    + \ \ \ \      +\ \ \ \  }

-a+2b+c

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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

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5x^2+x-11 from x^2-2x+8

x^2-2x+8

5x^2+x-11

\underline{-  \ \ \     -  \ \ \     + \ \ \ \ }

-4x^2-3x+19

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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

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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

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

First Add

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

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

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Q.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

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Q.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

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Q.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

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Q.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

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Q.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  

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