CLASS 8 MATHS CHAPTER-9 ALGEBRAIC EXPRESSIONS AND IDENTITIES

Exercise 9.1

Question 1.

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

(i)    

(ii) 1 + x + x²

(iii)

(iv)3 – pq + qr -rp

(v)+  – xy

(vi) 3 – pq + qr -rp

Solution :

(i) Terms: and 

Coefficient inis 5 and in  is  -3

(ii) Terms: 1, x and x²

Coefficient ofand coefficient of x²  is 1.

(iii) Terms: and  z²

Coefficient inis 4, coefficient of  is -4  and coefficient of z² is 1.

(iv) Terms: 3, -pq, qr  and -rp

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

(v) Terms: and  -xy

Coefficient of is coefficient of is  and coefficient of -xy is -1.

(vi) Terms: 0.3a, -0.6ab and 0.5b

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:

Solution :

 (i) Since  contains two terms. Therefore it is binomial.

(ii) Since 1000 contains one terms. Therefore it is monomial.

(iii) Sincecontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(iv) Since contains three terms. Therefore it is trinomial.

(v) Sincecontains two terms. Therefore it is binomial.

(vi) Since contains three terms. Therefore it is trinomial.

(vii) Sincecontains three terms. Therefore it is trinomial.

(viii) Sincecontains two terms. Therefore it is binomial.

(ix) Sincecontains four terms. Therefore it is a polynomial and it does not fit in above three categories.

(x) Since pqr contains one terms. Therefore it is monomial.

(xi) Sincecontains two terms. Therefore it is binomial.

(xii) Since  2p + 2q contains two terms. Therefore it is binomial.

Question 3.

Add the following:

(i)

(ii)

(iii)

(iv) 

Solution :

 (i)

Hence the sum if 0.

Hence the sum is  ab + ac + bc.

Question 4.

Solution :

NCERT Solutions for Class 8 Maths Exercise 9.2

Question 1.

Find the product of the following pairs of monomials:

(i)

(ii)    

(iii)

(iv)   

(iv) 4p ,0

Solution :

(i)  =  = 

(ii)=

=

(iii)= 

=

(iv) =

=

(v)=  = 0

Question 2.

Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively:

Solution :

 (i)   Area of rectangle

=

= sq. units

(ii) Area of rectangle

=

=

= 50mn sq. units

(iii) Area of rectangle  =

=

=sq. units

(iv) Area of rectangle  = 

=

= sq. units

(v) Area of rectangle  =

=

=sq. units

Question 3.

Complete the table of products:

(i)
    

Solution :

(i)
    

Question 4.

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

(i)    

(ii)

(iii)    

(iv)

Solution :

(i) Volume of rectangular box

=

=cubic units

(ii) Volume of rectangular box

=

= cubic units

(iii) Volume of rectangular box

=

=cubic units

(iv) Volume of rectangular box

=

= cubic units

Question 5.

Obtain the product of:

(i)

(ii)

(iii)   

(iv)

(v)

Solution :

(i)  

=

(ii)= 

=

(iii)

=

(iv)

=

(v)

=

NCERT Solutions for Class 8 Maths Exercise 9.3

Question 1.

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

(i)  

(ii)

(iii)

(iv)

(v)  

Solution :

(i)

=

(ii)

=

(iii)

=

(iv)

=

 (v) = 

= 0 + 0 + 0 = 0

Question 2.

Complete the table:

Solution :

Question 3.

Find the product:

(i)  

(ii)

(iii)

(iv)

Solution :

 (i)

=

(ii)

=

=

(iii)

=

=

(iv) =

Question 4.

(a) Simplify:and find values for

(i)

(ii)

(b) Simplify:find its value for

(i)

(ii)

(iii)

Solution :

(a)

=

(i) For

=

= 108 – 45 + 3 = 66

(ii) For

=

=

=

(b)

=

(i)  For  a= 0,

=

= 0 + 0 + 0 + 5 = 5

(ii) For a = 1

=

= 1 + 1 + 1 + 5 = 8

(iii) For

=

= ==4

Question 5.

(a) Add: and

(b) Add:and

(c) Subtract:from

(d) Subtract: from 

Solution :

(a)

=

=

(b)+ 

=

=

=

(c)

=

=

=

(d)

=

=

=

=

=

=

NCERT Solutions for Class 8 Maths Exercise 9.4

Question 1.

Multiply the binomials:

(i)and

(ii)and

(iii)  and

(iv)and 

(v) and

(vi) and

Solution :

(i)

=

=

=

(ii)

= 

=

=

(iii)

=

=

=

(iv)

=

=

(v)

=

=

=

=

(vi)

=

=

=

Question 2.

Find the product:

(i) 

(ii)

(iii)

(iv)  

Solution :

(i)

=

== 15 – x -2x²

(ii)

=

=

(iii)

=

=

(iv)

=

=

Question 3.

Simplify:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Solution :

(i)

=

=

=

(ii)

=

=

=

(iii)

=

=

(iv)

=

=

=

= 4ac

(v)

=

=

=

(vi)

=

=

(vii)

=

=

=

(viii)

=

=

=