NCERT Solutions (Ex - 9.1,9.2,9.3) - Algebraic Expressions, Class 9, Maths - Class 8 PDF Download

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 z² is 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: 

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

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) 4p³, - 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); (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:

Answer 3: 

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: 

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: 

Question 2: 

Complete the table: 

Answer 2: 

Question 3: 

Find the product: 

Answer 3: 

Question 4: 

(a) Simplify: 

Answer 4: 

Question 5: 

Answer 5: