# NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities Exercise 9.1

## Introduction:

In this exercise/article we will learn about expressions, four terms Monomial, Binomial, trinomial, Polynomial and terms, factors and coefficients of addition and subtraction of algebraic expressions find out Monomial, Binomial, trinomial, Polynomial the numerical factor of a term is called its numerical coefficient or simply coefficient.

NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities :

- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.5

**Class 8 Maths Exercise 9.1 (Page-140)**

**Q1. **Identify the terms, their coefficients for each of the following expressions.

(i) 5xyz^{2} - 3zy

**Solution : **

We have given terms are 5xyz^{2} - 3zy

So, coefficients of 5xyz^{2} = 5

and coefficient of - 3zy = -3

(ii) 1+x+x^{2}

**Solution :**

We have given terms are 1+x+x^{2}

So, coefficient of 1 = 1

coefficient of x = 1

and coefficient of x^{2} = 1

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

**Solution :**

We have given terms are 4x^{2}y^{2}- 4x^{2}y^{2}z^{2}+z^{2}

So, coefficient of 4x^{2}y^{2} = 4

coefficient of - 4x^{2}y^{2}z^{2} = -4

and coefficient of z^{2} = 1

(iv) 3-pq+qr-rp

We have given terms are 3-pq+qr-rp

So, coefficient of 3 = 3

coefficient of -pq = -1

coefficient of qr = 1

and coefficient -rp = -1

(v) \(\displaystyle \frac{x}{2}+\frac{y}{2}-xy\)

**Solution :**

We have given terms are \(\displaystyle \frac{x}{2}+\frac{y}{2}-xy\)

So, coefficient of \(\displaystyle \frac{x}{2}\) = \(\displaystyle \frac{1}{2}\)

coefficient of = \(\displaystyle \frac{1}{2}\)

and coefficient of = -1

(vi) 0.3a - 0.6ab + 0.5b

**Solution :**

We have given terms are 0.3a - 0.6ab + 0.5b

So, coefficient of 0.3a = 0.3

coefficient of - 0.6ab = - 0.6

and coefficient of 0.5b = 0.5

**Q2. **Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do

not fit in any of these three categories?

x + y , 1000 , x + x^{2} + x^{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

**Solution :**

Monomials = 1000 , pqr

Binomials = x + y , 2y - 3y^{2} , 4z - 15z^{2} , p^{2}q + pq^{2} , 2p + 2q

Trinomials = 7 + y + 5x , 2y - 3y^{2} + 4y^{3} , 5x - 4y + 3xy

Polynomials = x + x^{2} + x^{3} + x^{4} , ab + bc + cd + da

## Class 8 Maths Chapter 9 Exercise 9.1

**Q3.**Add the following**.**

(i) ab - bc , bc - ca , ca - ab

**Solution :**

\(\displaystyle \begin{array}{l}\,\,\,ab-bc-ca\\-ab+bc+ca\\\overline{{\underline{{\,\,\,\,\,0\,\,\,+\,\,0\,\,+\,0\,\,\,\,\,}}}}\end{array}\)

**If you have any doubt then follow the step by steps Given below :**

( ab - bc ) + ( bc - ca ) + ( ca - ab )

= ab - bc + bc - ca + ca - ab

= ( ab - ab ) + ( - bc + bc ) + ( - ca + ca )

= (0) + (0) + (0)

= 0 + 0 + 0

= 0

( ii ) a - b + ab , b - c + bc , c - a + ac

**Solution :**

\(\displaystyle \begin{array}{l}\,\,\,a-b-c+ab+bc+ac\\-a+b+\,c\,+\,0\,+\,0\,+0\\\overline{{\underline{{\,\,\,0+\,0\,+0+\,ab+bc+ac\,}}}}\end{array}\)

**If you have any doubt then follow the step by steps Given below :**

a - b + ab + b - c + bc + c - a + ac

= ( a - b + ab ) + ( b - c + bc ) + ( c - a + ac )

= ( a - a ) + ( -b + b ) + ( -c + c ) + ( ab + bc + ac )

= ( 0 ) + ( 0 ) + ( 0 ) + ( ab + bc + ac )

= ab + bc + ac

(iii) 2p^{2}q^{2} - 3pq + 4 , 5 + 7pq - 3p^{2}q^{2}

**Solution :**

\(\displaystyle \begin{array}{l}\,\,\,\,\,\,2{{p}^{2}}{{q}^{2}}-3pq+4\text{ }\\-\text{ }3{{p}^{2}}{{q}^{2}}+7pq+5\\\overline{{\underline{{\,\,-{{p}^{2}}{{q}^{2}}+\,4pq\,+9}}}}\,\end{array}\)

**If you have any doubt then follow the step by steps Given below :**

2p^{2}q^{2} - 3pq + 4 + 5 + 7pq - 3p^{2}q^{2}

= ( 2p^{2}q^{2} - 3p^{2}q^{2} ) + ( - 3pq + 7pq ) + ( 4 + 5 )

= ( - p^{2}q^{2} ) + ( 4pq ) + ( 9 )

= - p^{2}q^{2} + 4pq + 9

(iv) l^{2 } + m^{2} , m^{2} + n^{2} , n^{2} + l^{2} , 2lm + 2mn + 2nl

**Solution :**

\(\displaystyle \begin{array}{l}{{l}^{{2~}}}+{{m}^{2}}+{{n}^{2}}+2lm+2mn+2nl\\{{l}^{2}}+{{m}^{2}}+{{n}^{2}}\,\,+\,\,0\,\,\,+\,\,\,0\,\,\,+\,\,\,0\,\,\\\overline{{\underline{{2{{l}^{2}}+2{{m}^{2}}+2{{n}^{2}}+2lm+2mn+2nl}}}}\end{array}\)

**If you have any doubt then follow the step by steps Given below :**

l^{2 } + m^{2} + m^{2} + n^{2} + n^{2} + l^{2} + 2lm + 2mn + 2nl

= ( l^{2} + l^{2} ) + ( m^{2} + m^{2} ) + ( n^{2} + n^{2} ) + ( 2lm + 2mn + 2nl )

= ( 2l^{2} ) + ( 2m^{2} ) + ( 2n^{2} ) + ( 2lm + 2mn + 2nl )

= 2l^{2} + 2m^{2} + 2n^{2} + 2lm + 2mn + 2nl

= 2 ( l^{2} + m^{2} + n^{2} + lm + mn + nl )

**Q4. (a)** Subtract 4a - 7ab + 3b + 12 from 12a - 9ab + 5b - 3

**Solution : **

( 12a - 9ab + 5b - 3 ) - ( 4a - 7ab + 3b + 12 )

= 12a - 9ab + 5b - 3 - 4a + 7ab - 3b - 12

= 12a - 4a - 9ab + 7ab + 5b - 3b - 3 - 12

= 8a - 2ab + 2b - 15

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

**Solution :**

( 5xy - 2yz - 2zx + 10xyz ) - ( 3xy + 5yz - 7zx )

= 5xy - 2yz - 2zx + 10xyz - 3xy - 5yz + 7zx

= 5xy - 3xy - 2yz - 5yz + 7zx + 10xyz

= 2xy - 7yz + 7zx + 10xyz

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

**Solution :**

( 18 - 3p - 11q + 5pq - 2pq^{2} + 5p^{2}q ) - ( 4p^{2}q - 3pq + 5pq^{2} - 8p + 7q - 10 )

= 18 - 3p - 11q + 5pq - 2pq^{2} + 5p^{2}q - 4p^{2}q + 3pq - 5pq^{2} + 8p - 7q + 10

= 18 + 10 - 3p + 8p - 11q - 7q + 5pq + 3pq - 2pq^{2} - 5pq^{2} + 5p^{2}q - 4p^{2}q

= 28 + 5p - 18q + 8pq - 7pq^{2} + p^{2}q .

NCERT Solutions Class 8 Maths Chapter 9 Algebraic Expressions and Identities :

- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.1
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.2
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.3
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.4
- NCERT Class 8 Maths Algebraic Expressions and Identities Exercise 9.5