What is the most common careless mistake to be avoided here?

Checking the + and - signs is very important to avoid any mistakes with algebraic expressions.

Like terms contain the same variables, with the same powers. Coefficients can vary.

What is an example where we might apply such math expressions?

Multiplying algebraic expressions can be useful for finding the area of shapes when the sides are given as an expression.

CBSE Notes

Class 8

Maths

Chapter 8 Algebraic Expressions and Identities

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CBSE Class 8 Syllabus

CBSE syllabus outlines the topics and subtopics that will be covered in the exam, helping students focus on what’s important and avoid wasting time on irrelevant material.

CBSE Class 8 Notes

CBSE Class 8 Notes are important for students who want to prepare effectively for the exam. They are also helpful in...

CBSE Class 8: Complete Overview

The Central Board of Education (CBSE) administers the class 8 exam, a prerequisite for all NCERT-based schools to be affiliate...

NCERT Solutions Class 8

The NCERT Solutions for Class 8 provide systematically well-structured and very explanatory answers to all the questions included in NCERT Class 8 textbooks. These...

CBSE Exam

CBSE is a national-level board of education in India, responsible for public and private school education, and is managed by the Gover...

Important CBSE Maths Topics

Mathematics is the study of patterns, structure, and relationships, rooted in fundamental practices like counting...

CBSE Notes For Class 8 Maths Chapter 8 Algebraic Expressions And Identities

1.0Introduction

In earlier math classes, you might have learned how to add and subtract simple algebraic expressions. However, when it comes to slightly larger equations, properly arranging your equation, and the methods to write it down become more important. It also becomes necessary to understand the multiplication of such expressions.

The concept of monomials, binomials, trinomials, and polynomials is a must-know basis to easily learn the multiplication of algebraic expressions.

2.0Download Class 8 Maths Chapter 8 Algebraic Expressions and Identities : Free PDF

Download the free PDF of CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities to strengthen your understanding of key concepts. These notes cover important formulas, identities, and solved examples, making revision easier and more effective making it perfect for quick practice and exam preparation.

Class 8 Maths Chapter 8 Revision Notes:

3.0CBSE Class 8 Math Chapter 8 Algebraic Expressions and Identities- Revision Notes

How to Add and Subtract algebraic expressions?

Let us say we have to add the two expressions, 8x2+3x-4 and 10x+2. To subtract them, arrange them as follows:

$8 x^{2} + 3 x - 4 - 10 x + 2 8 x^{2} - 7 x - 6$

Here, it is important to note that in general math, (-4)-(+2) becomes (-4)-2, which is -6.

Multiplication of Monomials

Algebraic expressions that contain only one term are called monomials.

Multiplying two monomials

In simple terms, 5x=x+x+x+x+x=5x.
In the same way, 3(5x)=5x+5x+5x=15x.
Take an expression $5 x y \times 2 x y^{2} = (5 \times 2) \times (x y \times x y^{2})$ , which becomes $10 x^{2} y^{3}$
Here, the numbers are multiplied separately while the powers of variables are collected from the algebraic parts of both monomials.

Multiplying three or more monomials

With more than two monomials, focus on multiplying the first two monomials. The solution from multiplying the first two is then multiplied with the third monomial.
This method can fit as many monomials as required in your math problem.

Multiplication of Monomials and Polynomials

An expression with two terms is a binomial, three is a trinomial, and more than that is a polynomial.

Multiplying a monomial by a binomial:

Say we have to multiply the monomial 3x with a binomial 2x+y.
Here, we will have to use the distributive law for math, which makes it $3 x \times (2 x + y) = (3 x \times 2 x) + (3 x \times y) = 6 x^{2} + 3 x y .$

Multiplying a monomial by a trinomial:

Here, each term in the trinomial is multiplied by the monomial using distributive law. The products of this are then added together.
Multiply 3x by $x^{2} + 2 x + 4.$

$x \cdot (x^{2} + 2 x + 4) = (3 x \cdot x^{2}) + (3 x \cdot 2 x) + (3 x \cdot 4)$

$= 3 x^{3} + 6 x^{2} + 12 x$

Multiplying Polynomials

Multiplying a binomial by a binomial

This also follows the same distributive law. When multiplying polynomials, terms should always be identified and combined, if any.

Multiplying a binomial by a trinomial

Each of the three terms in the trinomial has to be multiplied by each of the two terms in the binomial.
Everything else follows the same rules of distribution as before.

4.0Solving Questions Related to Algebraic Expressions and Identities

Question 1: Simplify $5 x y \times 7 x^{2} y^{2} \times 8 x^{2} y^{2} \times 2 x y$

Solution:

$= 5 x y \times 7 x^{2} y^{2} \times 8 x^{2} y^{2} \times 2 x y = (5 x y \times 7 x^{2} y^{2}) (8 x^{2} y^{2} \times 2 x y)$

$= 35 (x^{3} y^{3}) \times 16 (x^{3} y^{3})$

$= 560 x^{6} y^{6}$

Question 2: Simplify (2x+3y)(3x+4y)

Solution:

$= 3 x \times (2 x + 3 y) + 4 y \times (2 x + 3 y)$

$= (3 x \times 2 x) + (3 x \times 3 y) + (4 y \times 2 x) + (4 y \times 3 y)$

$= 6 x^{2} + 9 y x + 8 y x + 12 y^{2}$

$= 6 x^{2} + 17 x y + 12 y^{2} .$

Question 3: Verify that (3x + 5y)² – 30xy = 9x² + 25y²

Solution: Taking L.H.S.

= (3x + 5y)² – 30xy

Taking identity (a + b)² = a² + 2ab + b²

= (3x)² + 2 × 3x × 5y + (5y)² – 30xy

= 9x² + 30xy + 25y² – 30xy

= 9x² + 25y²

L.H.S = R.H.S

Question 4: Verify that (11pq + 4q)² – (11pq – 4q)² = 176pq²

Solution:

L.H.S.

= (11pq + 4q)² – (11pq – 4q)²

= (11pq + 4q + 11pq – 4q) × (11pq + 4q – 11pq + 4q)

[using a² – b² = (a – b) (a + b), here a = 11pq + 4q and b = 11 pq – 4q]

= (22pq) (8q) = 176 pq²

L.H.S = R.H.S

5.0Key Features of CBSE Maths Notes for Class 8 Chapter 8

Notes are aligned with the latest CBSE math curriculum.
Easy to understand, with simple examples.
Crisp and short explanations for quick revision.
Notes are checked thoroughly and are 100% accurate.

6.0Sample Question on CBSE Maths Notes for Class 8 Chapter 8

Q1: How can we substitute values in these expressions?

Take this expression

$3 x \times (4 x^{2} + 5 x + 7) = (3 x \times 4 x^{2}) + (3 x \times 5 x) + (3 x \times 7) = 12 x^{3} + 5 x^{2} + 21 x .$

If you are instructed to solve it x=1 , you can simply substitute 1 as the value of x to obtain: 12(1)+5(1)+21(1)=38.

Chapter-wise CBSE Notes for Class 8 Maths:

Class 8 Maths Chapter 1 - Rational Numbers Notes

Class 8 Maths Chapter 2 - Linear Equations In One Variable Notes

Class 8 Maths Chapter 3 - Understanding Quadrilaterals Notes

Class 8 Maths Chapter 4 - Data Handling Notes

Class 8 Maths Chapter 5 - Squares and Square Roots Notes

Class 8 Maths Chapter 6 - Cubes and Cube Roots Notes

Class 8 Maths Chapter 7 - Comparing Quantities Notes

Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Notes

Class 8 Maths Chapter 9 - Mensuration Notes

Class 8 Maths Chapter 10 - Exponents and Powers Notes

Class 8 Maths Chapter 11 - Direct and Inverse Proportions Notes

Class 8 Maths Chapter 12 - Factorisation Notes

Class 8 Maths Chapter 13 - Introduction to Graphs Notes

Chapter-wise NCERT Solutions for Class 8 Maths All Chapters:-

Chapter 1: Rational Numbers

Chapter 2: Linear Equations in One Variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Data Handling

Chapter 5: Squares and Square Roots

Chapter 6: Cubes and Cube Roots

Chapter 7: Comparing Quantities

Chapter 8: Algebraic Expressions and Identities

Chapter 9: Mensuration

Chapter 10: Exponents and Powers

Chapter 11: Direct and Inverse Proportions

Chapter 12: Factorisation

Chapter 13: Introduction to Graphs

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Join ALLEN!

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I authorise ALLEN Career Institute Pvt Ltd to send me regular updates via Phone calls, Whatsapp, SMS, Robocalls (Automated Calls), Emails, or on postal address.

CBSE Class 8 Syllabus

CBSE syllabus outlines the topics and subtopics that will be covered in the exam, helping students focus on what’s important and avoid wasting time on irrelevant material.

CBSE Class 8 Notes

CBSE Class 8 Notes are important for students who want to prepare effectively for the exam. They are also helpful in...

CBSE Class 8: Complete Overview

The Central Board of Education (CBSE) administers the class 8 exam, a prerequisite for all NCERT-based schools to be affiliate...

NCERT Solutions Class 8

The NCERT Solutions for Class 8 provide systematically well-structured and very explanatory answers to all the questions included in NCERT Class 8 textbooks. These...

CBSE Exam

CBSE is a national-level board of education in India, responsible for public and private school education, and is managed by the Gover...

Important CBSE Maths Topics

Mathematics is the study of patterns, structure, and relationships, rooted in fundamental practices like counting...

CBSE Notes For Class 8 Maths Chapter 8 Algebraic Expressions And Identities

1.0Introduction

In earlier math classes, you might have learned how to add and subtract simple algebraic expressions. However, when it comes to slightly larger equations, properly arranging your equation, and the methods to write it down become more important. It also becomes necessary to understand the multiplication of such expressions.

The concept of monomials, binomials, trinomials, and polynomials is a must-know basis to easily learn the multiplication of algebraic expressions.

2.0Download Class 8 Maths Chapter 8 Algebraic Expressions and Identities : Free PDF

Download the free PDF of CBSE Class 8 Maths Chapter 8 Algebraic Expressions and Identities to strengthen your understanding of key concepts. These notes cover important formulas, identities, and solved examples, making revision easier and more effective making it perfect for quick practice and exam preparation.

Class 8 Maths Chapter 8 Revision Notes:

3.0CBSE Class 8 Math Chapter 8 Algebraic Expressions and Identities- Revision Notes

How to Add and Subtract algebraic expressions?

Let us say we have to add the two expressions, 8x2+3x-4 and 10x+2. To subtract them, arrange them as follows:

$8 x^{2} + 3 x - 4 - 10 x + 2 8 x^{2} - 7 x - 6$

Here, it is important to note that in general math, (-4)-(+2) becomes (-4)-2, which is -6.

Multiplication of Monomials

Algebraic expressions that contain only one term are called monomials.

Multiplying two monomials

In simple terms, 5x=x+x+x+x+x=5x.
In the same way, 3(5x)=5x+5x+5x=15x.
Take an expression $5 x y \times 2 x y^{2} = (5 \times 2) \times (x y \times x y^{2})$ , which becomes $10 x^{2} y^{3}$
Here, the numbers are multiplied separately while the powers of variables are collected from the algebraic parts of both monomials.

Multiplying three or more monomials

With more than two monomials, focus on multiplying the first two monomials. The solution from multiplying the first two is then multiplied with the third monomial.
This method can fit as many monomials as required in your math problem.

Multiplication of Monomials and Polynomials

An expression with two terms is a binomial, three is a trinomial, and more than that is a polynomial.

Multiplying a monomial by a binomial:

Say we have to multiply the monomial 3x with a binomial 2x+y.
Here, we will have to use the distributive law for math, which makes it $3 x \times (2 x + y) = (3 x \times 2 x) + (3 x \times y) = 6 x^{2} + 3 x y .$

Multiplying a monomial by a trinomial:

Here, each term in the trinomial is multiplied by the monomial using distributive law. The products of this are then added together.
Multiply 3x by $x^{2} + 2 x + 4.$

$x \cdot (x^{2} + 2 x + 4) = (3 x \cdot x^{2}) + (3 x \cdot 2 x) + (3 x \cdot 4)$

$= 3 x^{3} + 6 x^{2} + 12 x$

Multiplying Polynomials

Multiplying a binomial by a binomial

This also follows the same distributive law. When multiplying polynomials, terms should always be identified and combined, if any.

Multiplying a binomial by a trinomial

Each of the three terms in the trinomial has to be multiplied by each of the two terms in the binomial.
Everything else follows the same rules of distribution as before.