# NCERT Solutions For Class 8 Maths Chapter 9

## NCERT Solutions Class 8 Maths Algebraic Expressions and Identities

### Ncert Solutions For Class 8 Maths Chapter 9 PDF Free Download

NCERT Solutions for class 8 Maths chapter 9 Algebraic expression & Identities is crucial for the students of class 8 to excel in their examination. These solution help students to frame a better understanding of the topic. To ease the fear of maths, we at BYJU’S provide NCERT Solution for Class 8 Maths Chapter 9 Algebraic Expressions. Student can download the NCERT Solution for class 8 Maths Chapter 9 pdf or can view it online by following the link. These solution are provided in detailed manner, where one can find step-by-step solution to all the questions of NCERT class 8 maths chapter 9 NCERT Solutions.

### NCERT Solutions Class 8 Maths Chapter 9 Exercises

Before going into the details of the Algebraic expression and identities, let us understand what are expression and how are they different from an equation.

The following are the examples of expression:

4x – 3, 3x2 – 5x + 2

An expression need not be equal to any value, as in case of equation.

In this chapter we will learn about the different properties, and operation of an expression, such as adding, subtracting, multiplying and dividing expressions etc. There can be various types of multiplication of an expression, such as multiplying monomial with monomial, binomial, or even polynomial with polynomial. Along with these multiplication, we will learn about the various identities.

An identity of an equation is the one which holds true for the left hand side and the right hand side of an equation, i.e.  such as, an equality, true for every value of the variable in it, is called an identity. There are various standard identities for an algebraic equation, few of them are given as-

(a+b)2 = a2 + 2ab + b2

(a-b)2 = a2 – 2ab + b2

(a-b) (a+b)= a2 – b2

We use all these identities in solving an algebraic expression or determining the value of the variable. For the students of class 8, it is essential to have a good hold of this chapter, Algebraic  expression and identities so as to have a better learning experience, as well as from the examination point of view, one need to have a good understanding of this chapter to excel in the examination. As being one of the most important topic for the students of class 8, one can expect various questions from this chapter in their final examination. Also, this chapter holds importance in the higher standards as well, as we study about this chapter in more detail. Thus one need to have a thorough understanding for this chapter.

Below given is the NCERT Solution for Algebraic expression and Identities, so that students can refer to various difficult questions of this chapter and clear all their doubts.

Exercise 9.1

Q.1. Identify the terms and their coefficients for each of the following expressions.

(I) 5abc2 – 3cb

Terms :  5abc2

3cb

Coefficients: 5, -3

(II) 1+a+a2

Terms: 1, a, a2

Coefficients: 1, 1, 1

(III) 4x2y– 4 x2y2z+  z2

Terms: 4x2y2   ,  -4 x2y2z2    ,  Z2

Coefficient: 4,  -4,  1

(IV) 3 – xy + yz – zx

Terms:   3:  -xy,  yz,  -zx

Coefficient:  3:  -1,  1,  -1

(V) $\frac{a}{2}+\frac{b}{2}-ab$

Terms: $\frac{a}{2}$,  $\frac{b}{2}$,  -ab

Coefficient: $\frac{1}{2}$,  $\frac{1}{2}$,  -1

(VI)0.3x-0.6xy+0.5y

Terms: 0.3x,  -0.6xy,  0.5y

Coefficient: 0.3,  -0.6,  0.5

Q.2. Check whether the following polynomials are monomials, binomials or trinomials. Find out which polynomials do not fit any of these three categories?

1)  x+y,

2)  1000,

3)  $x+x^{2}+x^{3}+x^{4}$,

4)  7+y+5x,

5)  $2y-3y^{2}$,

6)  $2y-3y^{2}+4y^{3}$,

7)  5x-4y+3xy,

8)  $4z-15z^{2}$,

9)  ab+bc+cd+da,

10)  pqr,

11)  $p^{2}q+pq^{2}$,

12)  2p+2q,

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 that do not fit any of these categories are :

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

Q.3.Add the following :

Note: The given expressions written in separate rows, with like terms one below the other and then the addition of these expressions are done.

(I)ab – bc,    bc – ca,    ca – ab

ab-bc

+   bc-ca

+  -ab+ca

=           0

(II) x – y+xy,       y-z+yz,        z-x+xz

x – y + xy

+      y -z+yz

+       -x+z +xz

=        xy+yz+xz

(III) $2a^{2}b^{2}-3ab+4\, \, \, 5+7ab-3a^{2}b^{2}$

$2a^{2}b^{2}-3ab+4$

+    $-3a^{2}b^{2}+7ab+5$

$-a^{2}b^{2}+4ab+9$

(IV) $a^{2}+b^{2}\, \, \, b^{2}+c^{2},\, \, \, c^{2}+a^{2},\, \, \, 2ab+2bc+2ca$

$a^{2}+b^{2}$

+     $b^{2}+c^{2}$

+     $c^{2}+a^{2}$

+     2ab+2bc+2ca

=      $2a^{2}+2b^{2}+2c^{2}+2ab+2bc+2ca$

Q.4. (i)Substract 4x-7xy+3y+12 from 12x-9xy+5y-3

12x – 9xy + 5y –  3

4x – 7xy + 3y + 12

(-)     (+)    (-)    (-)

8x – 2xy + 2y – 15

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

5xy – 2yz -2zx +10xyz

3xy + 5yz -7zx

(-)      (-)      (+)

2xy-7yz + 5zx  +10xyz

(iii) $Substract\: 4p^{2}q-3pq+5pq^{2}-8p+7q-10 \:\, from\: \, 18-3p+11q+5pq-2pq^{2}+5p^{2}q$

$18-3p-11q+5pq-2pq^{2}+5p^{2}q$

$-10-8p+7q-3pq+5pq^{2} +4p^{2}q$

(+)          (+)   (-)  (+)   (-)            (-)

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

Exercise: 9.2

Q.1.For the following pairs of monomials find the product.

(I)5, 6a

Answer: $5\times 6\times a\\ =30a$

(II)-5a, 6 a

Answer: $-5a\times 6a\times \\ =-5\times a\times 6\times a\\ =(-5\times 6)\times (a\times a)\\ =-30a^{2}$

(III) )-5a, 6 ab

Answer: $-5a\times 6ab\times \\ =-5\times a\times 6\times a \times b\\ =(-5\times 6)\times (a\times a\times b)\\ =-30a^{2}b$

(IV) ) $5a^{3}$,- 4 a

Answer: $5a^{3}\times -4a \\ =5\times (-4)\times a\times a\times a \times a\\ =-20a^{4}$

(V)5a, 0

Answer: $5a\times 0\\ =5\times a\times 0\\ =0$

Q.2.calculate the area of rectangles.Where the pairs of monomials  are lengths and breadths respectively.

NOTE: area of rectangle =$length \times breadth$

• (a, b)

Area= $a \times b\\ =ab$

• (10a, 5b)

Area = $10a \times 5b\\ =10\times 5\times a\times b\\ =50ab$

• ($20p^{2},5q^{2}$)

Area = $20p^{2}\times 5q^{2}\\ =20\times 5\times p^{2}\times q^{2}\\ =100p^{2}q^{2}$

• ($4a,3a^{2}$)

Area = $4a\times 3a^{2}\\ =4\times 3\times a\times a^{2}\\ =12a^{3}$

• (4ab,3bc)

Area= $4ab\times 3bc\\ =4\times 3\times a\times b\times b\times c\\ =12ab^{2}c$

Q.3.Complete the table of product.

 First monomial Second monomial 2x -5y $3x^{2}$ -4xy $7x^{2}y$ $-9x^{2}y^{2}$ 2x $4x^{2}$ -5y $-15x^{2}y$ $3x^{2}$ -4xy

Solution:

 First monomial Second monomial 2x -5y $3x^{2}$ -4xy $7x^{2}y$ $-9x^{2}y^{2}$ 2x $4x^{2}$ $-10xy$ $6x^{3}$ $-8x^{2}y$ $14x^{3}y$ $18x^{3}y^{2}$ -5y $-10xy$ $-15x^{2}y$ $-15x^{2}y$ $20xy^{2}$ $-35x^{2}y^{2}$ $45x^{2}y^{3}$ $3x^{2}$ $6x^{3}$ $-15x^{2}y$ $9x^{4}$ $-12x^{3}y$ $21x^{4}y$ $-27x^{4}y^{2}$ -4xy $-8x^{2}y$ $20x^{2}y$ $-12x^{3}y$ $16x^{2}y^{2}$ $-28x^{3}y^{2}$ $36x^{3}y^{3}$

Q.4.Rectangular boxes with the length $,$breadth $,$ and height are given respectively. Find the volume.

(I) $5x, 3x^{2}, 7x^{4}$

Answer: $Volume=5x\times 3x^{2}\times 7x^{4}=5\times 3\times 7\times x\times x^{2}\times x^{4}=105x^{7}$

(II)2p, 4q, 8r

Answer: $Volume=2p\times 4q\times 8r= 2\times 4\times 8\times p\times q \times r=64pqr$

(III) $ab, 2a^{2}b, 2ab^{2}$

Answer:  $Volume=ab\times 2a^{2}b\times 2ab^{2}=2\times 2\times ab\times a^{2} b\times ab^{2}=4a^{4}b^{4}$

(IV)p, 2q, 3r

Answer:  $Volume=p\times 2q\times 3r= 2\times 3\times p\times q \times r=6pqr$

Q.5.Find the Product of the following:

(I)ab, bc, ca

Answer: $ab\times bc\times ca$= $a^{2}b^{2}c^{2}$

(II) $x, -x^{2}, x^{3}$

Answer: $x\times (-x^{2})\times x^{3}=-x^{6}$

(III) $2, 4a, 8a^{2}, 16a^{3}$

Answer: $2\times 4a\times 8a^{2}\times 16a^{3}=1024a^{6}$

(IV)x, 2y, 3z, 6xyz

Answer: $x\times 2y\times 3z\times 6xyz=36x^{2}y^{2}z^{2}$

(V)m, -mn, mnp

Answer: $m\times -mn\times mnp=-m^{3}n^{2}p$

#### Practise This Question

For vacation, Ted was going to a hill station. When he started, he checked out the Odometer of his dad’s car. The reading was 1111.22 km. After the journey, the reading was 1342.56 km. How many meters did Ted travel through?