Revise notes Class 8 algebraic expressions and identities

Revise notes
Class 8 Maths
Algebraic Expressions and Identities

Topics

1. Introduction
2. Terms, Factors and Coefficients
3. Monomials, Binomials and Polynomials
4. Like and Unlike Terms
5. Addition and Subtraction of Algebraic Expressions
6. Multiplication of Algebraic Expressions
7. Introduction
8. Multiplying a Polynomial by a Polynomial
9. Terms, Factors and Coefficients
10. Standard Identities
11. Monomials, Binomials and Polynomials
12. Like and Unlike Terms
13. Addition and Subtraction of Algebraic Expressions
14. Multiplication of Algebraic Expressions
15. Multiplying a Monomial by a Polynomial
16. Multiplying a Polynomial by a Polynomial
17. Standard Identities

Terms, Factors and Coefficients

Terms are added to form an expression.

Ex: terms 3x and 7 are added to form the expression 3x + 7

Again, the expression 2y² – 7xy are formed by adding the terms 2y² and -7xy i.e.

2y² + (-7xy) = 2y² – 7xy

Factors of a term

A term is a product of its factors.

Let us take a term 2y²

The term 2y² is a product of 2, y and y. Now, we say that 2, y and y are the factors of the term 2y²

Again the term – 7xy is a product of the factors -7, x and y.

Coefficient

The numerical factor is said to be the numerical coefficient or simply the coefficient of the term.

Ex: In the term 20y², 20 is the coefficient of y².

Again, in the term -3xyz, -3 is the coefficient of xyz.

In general, a coefficient may be either a numerical factor or an algebraic factor or a product of two or

more factors.

Ex: In the term 7xy, 7 is the coefficient of xy, x is the coefficient of 7y and y is the coefficient of 7x.

In 5xy², 5 is the coefficient of xy², x is the coefficient of 5y² and y² is the coefficient of 5x.

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

(i) 5xyz² - 3zy (ii) 1+ x + x² (iii) 4x² y² - 4x² y² z²

(iv) 3 - pq + qr - rp (v) x/2 + y/2 - xy (vi) 0.3a - 0.6ab + 0.5b

Solution:

(i) Terms: 5xyz² and -3zy

Coefficient in 5xyz² is 5 and in -3zy is -3.

(ii) Terms: 1, x and x².

Coefficient of x and coefficient of x² is 1.

(iii) Terms: 4x² y², -4 x² y² z² and z².

Coefficient in 4x² y² is 4, coefficient of -4 x² y² z² 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 -1.

(v) Terms: x/2, y/2 and and -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 0.5b

Coefficient of 0.3a is 0.3, coefficient of -0.6ab is -0.6 and coefficient of 0.5b is 0.5.

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Class 8 Maths Algebraic Expressions and Identities NCERT Chapter 9 Free Notes for Best Revision

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