NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

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Class 8 : NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

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Exercise 9.1 

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

[i] 5xyz2 - 3zy

[ii] 1 +x+ x2

(iii) 4x2y2 - 4x2y2z2 + z2 

[iv] 3 - pq + qr — rp

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

[vi] 0.3a - 0.6ab + 0 5b

Answer 1:

(i)

Terms: 5xyz2 - 3zy

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

(ii)

Terms:  1 +x+ x2

Coefficient of x and coefficient of x2 is 1.

(iii)

Terms: 4x2y2 - 4x2y2z2 + z2 

Coefficient in 4x2y2 is 4, coefficient of -4x2y2z2 is -4 and coefficient of zis 1.

[iv]

Terms: 3 - pq + qr — 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 -0.6ab 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: 

  1. x + y
  2. 1000, 
  3. x + x2 + x3 + x4
  4. 7 +y + 5x, 
  5. 2y-3y2
  6. 2y-3y2 + 4y3
  7. 5x-4y+3xy, 
  8. 4z-15z2
  9.  ab + bc + cd + da,
  10. pqr
  11. p2q + pq2
  12. 2p + 2q

Answer 2:

  1. Since x + y contains two terms. Therefore it is binomial.
  2. Since 1000 contains one terms. Therefore it is monomial.
  3. Since x + x2 + x2 +x4 contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
  4. Since 7 y + 5x contains three terms. Therefore it is trinomial.
  5. Since 2y-3y2 contains two terms. Therefore it is binomial.
  6. Since 2y-3y2 + 4y3  contains three terms. Therefore it is trinomial.
  7. Since 5x-4y 3xy contains three terms. Therefore it is trinomial.
  8. Since 4x -15y2 contains two terms. Therefore it is binomial.
  9. Since ab+hc+cd da contains four terms. Therefore it is a polynomial and it does not fit in above three categories.
  10. Since pqr contains one terms. Therefore it is monomial.
  11. Since p2q + pq2 contains two terms. Therefore it is binomial.
  12. Since 2p + 2q contains two terms. Therefore it is binomial

Question 3:

Add the following: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Answer 3:

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

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 4p2q - 3pq + 5pq2 - 8p + 7q - 10 from 18- 3p-11q+5pq-2qp2 + 5 p2q

Answer 4:

(a) 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

(b)

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

(c)

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Exercise 9.2 

Question 1: 

Find the product of the following pairs of monomials: 

(i) 4, 7p

(ii) -4p, 7p

(iii) - 4p, 7pq

(iv) 4p3, - 3p

(v) 4p, 0

Answer 1:

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

 

Question 2: 

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:
 (p,q); (10m,5n); (20x2,5y2); (4x,3x2); (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

= 20x2 x 5y2 = (20 x 5 ) (x2 x y2) = 100x2y2 sq. units

(iv) Area of rectangle = length x breadth

= 4x x 3x2 = (4x3)(x x x2 ) sq. units

(v) Area of rectangle = length x breadth

= 3mn x 4np = (3x4)(mn x np) = 12mn2p sq. units

Question 3: 

Complete the table of products:

First monomial  →

Second monomial 

2x

—5y

3x2

-4 xy

7x2y

-9 x2y2

2x

4x2

.....

.....

.....

.....

.....

-5y

.....

.....

-15x2y

.....

.....

.....

3x2

.....

.....

.....

.....

.....

.....

-4 xy

.....

.....

.....

.....

.....

.....

7x2y

.....

.....

.....

.....

.....

.....

-9x2y2

.....

.....

.....

.....

.....

.....

 

Answer 3: 

 

First monomial  →

Second monomial 

2x

—5y

3x2

-4 xy

7x2y

-9 x2y2

2x

4x2

-10xy

6x3

-8x2y

14x3y

-18x3y2

-5y

-10xy

25 y2

-15x2y

20 xy2

-35x2y2

-45 x2y3

3x2

6x3

-15x2y

9x4

-12x3y

21 x4y

-27 x4y2

-4 xy

8x2y

20 xy2

-12x3y

16x2y2

-28 x3y2

36 x3y3

7x2y

14x3y

-35 x2y2

21 x4y

-28x3y2

49 x4y2

-63 x4y3

-9x2y2

-18x3y2

45x2y3

-27 x4y2

36 x3y3

-63x4y3

81 x4y4

 

Question 4: 

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

(i) 5a, 3a27a4

(ii) 2p,4q18r

(iii) xy, 2x2y, 2xy2

(iv) a, 2b, 3c

Answer 4: 

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

= 5a x 3 a2 x 7a4 = ( 5x3x7)(a x a2 x a4)

= I05a7 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, 2x2y, 2xy2  = (1 x 2 x 2 )(x x x2 x yx yx y2)

= 4x4 y2 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, -a2, a3

(iii) 2, 4y, 8y2, 16y3

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

(v) m, -mn,mnp 

Answer 5: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

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, 7a2b2

(iv) a2- 9, 4a

(v) pq+qr+rp,0

Answer 1: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

 

Question 2: 

Complete the table: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Answer 2: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

 

Question 3: 

Find the product: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Answer 3: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

 

Question 4: 

(a) Simplify: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Answer 4: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

 

Question 5: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

Answer 5: 

NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths Class 8 Notes | EduRev

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