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**Exercise 9.1 **

**Question 1: Identify the terms, their coefficients for each of the following expressions: **

[i] 5xyz^{2} - 3zy

[ii] 1 +x+ x^{2}

(iii) 4x^{2}y^{2} - 4x^{2}y^{2}z^{2} + z^{2}

[iv] 3 - pq + qr â€” rp

(v) x/2 + y/2 - xy

[vi] 0.3a - 0.6ab + 0 5b

**Answer 1:**

(i)

Terms: 5xyz^{2} - 3zy

Coefficient in x is 5 and in -3*zy* is -3

(ii)

Terms: 1 +x+ x^{2}

Coefficient of *x* and coefficient of *x ^{2}* is 1.

(iii)

Terms: 4x^{2}y^{2} - 4x^{2}y^{2}z^{2} + z^{2}

Coefficient in 4x^{2}y^{2} is 4, coefficient of *-4x ^{2}y^{2}z^{2}* is -4 and coefficient of z

[iv]

Terms: 3 - pq + qr â€” rp

Coefficient of *-pq* is -1, coefficient of *qr* is 1 and coefficient of *-rp* is -1.

[v]

Terms : x/2 , y/2 , -xy

Coefficient of x/2 is 1/2, coefficient of y/2 is 1/2 and coefficient of *-xy* is -1.

[vi]

Terms: 0.3a,-0.6ab and 0.56

Coefficient of 0.3a is 0.3, coefficient of -0.6*ab* is -0.6 and coefficient of 0.5b is 0.5

**Question 2: **

**Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any of these three categories: **

*x + y*,**1000,****x +***x*+ x^{2}^{3}+ x^{4},**7 +y + 5x,****2y-3y**^{2},**2y-3y**^{2}+ 4y^{3},**5x-4y+3xy,****4z-15z**^{2},*ab + bc + cd + da,**pqr*,*p*^{2}q + pq^{2},*2p + 2q*

**Answer 2:**

- Since
contains two terms. Therefore it is binomial.*x + y* - Since 1000 contains one terms. Therefore it is monomial.
- Since
*x + x*^{2}+ x^{2}**+x**^{4}contains four terms. Therefore it is a polynomial and it does not fit in above three categories. - Since 7
**+**+ 5x contains three terms. Therefore it is trinomial.*y* - Since
contains two terms. Therefore it is binomial.*2y-3y*^{2} - Since
**2y-3y**contains three terms. Therefore it is trinomial.^{2}+ 4y^{3} - Since 5x-4y
**+**3xy contains three terms. Therefore it is trinomial. - Since 4x -15y
^{2}contains two terms. Therefore it is binomial. - Since
*ab+hc+cd**+*contains four terms. Therefore it is a polynomial and it does not fit in above three categories.*da* - Since
contains one terms. Therefore it is monomial.*pqr* - Since
contains two terms. Therefore it is binomial.*p*^{2}q + pq^{2} - Since
contains two terms. Therefore it is binomial*2p + 2q*

**Question 3:**

**Add the following: **

**Answer 3:**

**Question 4: **

**(a) Subtract 4a-7zb + 3b + 12 from 12a-9ab+5b-3**

**(b) Subtract 3xy + 5yz - 7zx from 5xy - 2yz - 2zx + 10 xyz**

**(c) Subtract 4p ^{2}q - 3pq + 5pq^{2} - 8p + 7q - 10 from 18- 3p-11q+5pq-2qp^{2} + 5 p^{2}q**

**Answer 4:**

**(a) **

(b)

(c)

**Exercise 9.2 **

**Question 1: **

**Find the product of the following pairs of monomials: **

**(i) 4, 7p**

**(ii) -4p, 7p**

**(iii) - 4p, 7pq**

**(iv) 4p ^{3}, - 3p**

**(v) 4p, 0**

**Answer 1:**

**Question 2: **

**Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively: (p,q); (10m,5n); (20x ^{2},5y^{2}); (4x,3x^{2}); (3mn,4np)**

**Answer 2:**

[i] Area of rectangle = length x breadth

= pxq = pq sq. units

[ii] Area of rectangle = length x breadth

= 10m x 5n = (10x5)(mxn) = 50 mn sq. units

[iii] Area of rectangle = length x breadth

= 20x^{2} x 5y^{2} = (20 x 5 ) (x^{2} x y^{2}) = 100x^{2}y^{2} sq. units

(iv) Area of rectangle = length x breadth

= 4x x 3x^{2} = (4x3)(x x x^{2} ) sq. units

(v) Area of rectangle = length x breadth

= 3mn x 4np = (3x4)(mn x np) = 12mn^{2}p sq. units

**Question 3: **

**Complete the table of products:**

First monomial â†’ Second monomial | 2x | â€”5y | 3x | -4 xy | 7x | -9 x |

2x | 4x | ..... | ..... | ..... | ..... | ..... |

-5y | ..... | ..... | -15x | ..... | ..... | ..... |

3x | ..... | ..... | ..... | ..... | ..... | ..... |

-4 xy | ..... | ..... | ..... | ..... | ..... | ..... |

7x | ..... | ..... | ..... | ..... | ..... | ..... |

-9x | ..... | ..... | ..... | ..... | ..... | ..... |

**Answer 3: **

First monomial â†’ Second monomial | 2x | â€”5y | 3x | -4 xy | 7x | -9 x |

2x | 4x | -10xy | 6x | -8x | 14x | -18x |

-5y | -10xy | 25 y | -15x | 20 xy | -35x | -45 x |

3x | 6x | -15x | 9x | -12x | 21 x | -27 x |

-4 xy | 8x | 20 xy^{2} | -12x | 16x | -28 x | 36 x |

7x | 14x | -35 x | 21 x | -28x | 49 x | -63 x |

-9x | -18x | 45x | -27 x | 36 x | -63x | 81 x |

**Question 4: **

**Obtain the volume of rectangular boxes with the following length, breadth and height respectively: **

**(i) 5a, 3a ^{2}7a^{4}**

**(ii) 2p,4q18r**

**(iii) xy, 2x ^{2}y, 2xy^{2}**

**(iv) a, 2b, 3c**

**Answer 4: **

(i) Volume of rectangular box = length x breadth x height

= 5a x 3 a^{2} x 7a^{4} = ( 5x3x7)(a x a^{2} x a^{4})

= I05a^{7} cubic units

(ii) Volume of rectangular box = length x breadth x height

= 2p x 4 q x 8r = ( 2x4x8)(pxqxr)

= 64 pqr cubic units

(iii) Volume of rectangular box = length x breadth x height

= xy, 2x^{2}y, 2xy^{2}** ^{ }** = (1 x 2 x 2 )(x x x

= 4x^{4} y^{2} cubic units

(iv)

Volume of rectangular box = length x breadth x height

= a x 2b x 3c = (1x2x3) (axbxc) 6abc cubic units

**Question 5: **

**Obtain the product of:**

**(i) xy,yz,zx**

**(ii) a, -a ^{2}, a^{3}**

**(iii) 2, 4y, 8y ^{2}, 16y^{3}**

**(iv) a,2b,3c,6abc**

**(v) m, -mn,mnp**

**Answer 5: **

**Exercise 9.3 **

**Question 1: **

**Carry out the multiplication of the expressions in each of the following pairs: **

**(i) 4p,q+r**

**(ii) ab, a-b**

**(iii) a+ b, 7a ^{2}b^{2}**

**(iv) a ^{2}- 9, 4a**

**(v) pq+qr+rp,0**

**Answer 1: **

**Question 2: **

**Complete the table: **

**Answer 2: **

**Question 3: **

**Find the product: **

**Answer 3: **

**Question 4: **

**(a) Simplify: **

**Answer 4: **

**Question 5: **

**Answer 5: **

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