# NCERT Solutions For Class 8 Maths Chapter 9

## 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 8th class to excel in their examination. These solution help students to frame a better understanding of the topic and they can even download them in PDF for free. Students can download these pdf files and start practising it to score good marks in their final exams, in 2019. These solutions help students to frame a better understanding of the topic.

We at BYJU’S provide here, NCERT Solution for Class 8 Maths Chapter 9 Algebraic Expressions, prepared by subject experts. The student can either download these NCERT solutions or can view it online by following the link. These solutions are the best learning materials to practice perfectly for the exams, apart from sample papers and previous year question papers.

## Class 8 Maths NCERT Solutions for Algebraic Expressions and Identities

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 a polynomial. Along with multiplication, we will learn about the various identities. Here are the list of concepts:

• Brief introduction on Algebraic Expressions And Identities
• Define Expressions
• What are Terms, Factors, And Coefficients?
• Questions on Monomials, Binomials, And Polynomials
• What are Like And Unlike Terms?
• Algebraic Expressions Addition And Subtraction Methods
• Introduction to Multiplication Of Algebraic Expressions
• How to Multiply A Monomial By A Monomial
• How to Multiply A Monomial By A Polynomial
• How to Multiply A Polynomial By A Polynomial
• Define Identity
• What are Standard Identities
• Howe to Apply Identities

Students of Class 8 can also find exemplar problems available here online, for more practice on different types of questions asked from chapter 9, Algebraic expression & Identities. These materials are always available for students who have registered with us. All these NCERT materials such as books, notes, question paper are designed as per the CBSE syllabus (2018-2019) prescribed by the board for class 8.

### 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.

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 expressions and identities, as these basic formulas and identities will be used in higher classes as well. As being an important topic, one can expect various types of questions based on the formulas, from this chapter in their final examination.

#### 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

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

Bottom Line:

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