Algebraic expressions for class 8

Algebraic expressions for class 8 DEFAULT

Algebra Formulas for Class 8: Check Algebraic Identities

Algebra Formulas For Class 8: We have compiled important algebra formulas for Class 8. These formulas and algebraic identities will help all Class 8 students in their studies as well as final exams. 

Algebra is a broad part of mathematics in which we study about mathematical symbols and the rules for manipulating these symbols. Different symbols and letters are used to represent quantities and numbers. These symbols are used in equations and formulae to solve different mathematical problems. Algebra has many real-life applications in different fields including mathematics, science, engineering, medicine, and economics.

Algebraic identities for Class 8 along with algebraic expressions are introduced in the CBSE curriculum. As it is one of the most important units for CBSE Class 8, we have provided the complete list of important Maths formulas for Class 8 Algebra on this page. Going through these formulas will help students learn the Algebra chapter and have a quick glance at all the formulas when needed. Embibe recommends all students to bookmark this page to access algebraic expressions and identities Class 8 formulas in one click.

List Of Algebra Formulas For Class 8

Students who are looking for the complete list of maths formulas for class 8 pdf for algebra can refer to this article. You can check the list in the table below:

1. a2 – b2 = (a – b)(a + b)
2. (a + b)2 = a2 + 2ab + b2
3. a2 + b2 = (a + b)2 – 2ab
4. (a – b)2 = a2 – 2ab + b2
5. (a + b)3 = a3 + b3 + 3ab(a + b)
6. (a – b)3 = a3 – b3 – 3ab(a – b)
7. a3 – b3 = (a – b)(a2 + ab + b2)
8. a3 + b3 = (a + b)(a2 – ab + b2)
9. x(a + b) = xa + xb
10. x(a – b) = xa – xb
11. (x – a)(x – b) = x2 – (a + b)x + ab
12. (x – a)(x + b) = x2 + (b – a)x – ab
13. (x + a)(x – b)= x2 + (a – b)x –ab
14. (x + a)(x + b)= x2 + (a + b)x + ab
15. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
16. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2zx

Almost all of the Class 8 Maths NCERT Solutions for algebra unit can be done using these formulas only.

Get detailed Math formula chart for Class 8 including Trigonometry, Mensuration, Profit & Loss, Probability, and Exponents below:

Algebraic Expression & Identities Class 8 Formulas

An algebraic identity is an equality that holds true for any values of variables. So, if we know the values to the left of an expression, using the algebraic identity, we can deduce the result. An algebraic expression contains two things – Variables and Constants. The value of variable changes in different expressions while the constant remains the same. 

Important Points Regarding Algebraic Expressions Formulas.

  1. A variable can take any value. The value of an expression change with the value chosen for variables it contains.
  2. A line has an infinite number of points. A variable can take any position on the number line.
  3. There are different types of algebraic expressions depending on the number of terms they contain: Expressions containing one, two and three terms are called monomial, binomial and trinomial expressions respectively.
  4. The numerical factor of a term is called its coefficient.
  5. An identity is standard equality which is true for all the values of the variables in the equality.

Examples On Algebraic Expressions Formulas For Class 8

Understand different algebraic identities for Class 8 with examples that we have provided below. These examples will help you memorise the Class 8 algebra formula that we provided above.

1) Find out the value of 52 – 32.

Solution: 52 – 32 is of the form: a2 – b2, where a=5, b=3. 
Since a2 – b2 = (a + b)(a – b), putting the values of a and b in this expression, we get:
52 – 32
= (5 + 3)(5 – 3)
= 8 x 2
= 16.
Hence, the answer is 16.

2) 43 × 42 =?

Solution: 43 × 42 is of the form: (am)(an), where a=4, m=3, and n=2.
Since (am)(an) = am+n, putting the values of a and b in this expression, we get:
43 × 42
= 43+2
= 45
= 1024.
Hence, the answer is 1024.

3) Evaluate the value of (95)2 using identities.

Solution: 952 can be written as (100-5)2.
This can be expressed as (a-b)2, where a=100, b=5.
Since (a-b)2 = a2 -2ab +b2, putting the values of a and b in this expression, we get:
952
= (100-5)2
= 1002 – 2 x 100 x 5 + 52
= 10000 – 1000 + 25
= 9025.
Hence, the answer is 9025.

4) What is the value of x2 + y2 – 10 at x = 0 and y = 0?

Solution: x2 + y2 – 10,
Putting x = 0 and y = 0 in the expression, we get: 
02 + 02 – 10
= 0 – 10
= -10
Hence, the answer is -10.

5) Simplify (a + b + c)(a + b – c)

Solution: Using the algebraic expression:  x(a+b) = xa + xb, we can simplify the equation as follows:
(a+b+c)(a+b-c)
= a(a+b-c) +b(a+b-c) +c(a+b-c)
= axa + axb – axc + bxa + bxb – bxc + cxa + cxb – cxc 
= a2 + ab – ac + ba + b2 – bc + ca + cb – c2 
= a2 + b2 – c2 + ab + ba + ca – ac – bc + cb 
= a2 + b2 – c2 + 2ab

Now that we have provided algebraic formulas for class 8 with examples, let’s practice some important questions related to algebraic formulas and expressions.

Practice Questions On Formula Of Algebra Class 8

Here we have provided some of the practice questions on Algebra chapter for CBSE Class 8. These questions will brush up your concepts and help you memorise the algebra formula that we provided above.

Question 1: Classify the following polynomials as monomials, binomials, trinomials. Which polynomials do not fit in any category?

(i) x+y(ii) 1000
(iii) x+x2+x3+x4(iv) 7+a+5b
(v) 2b-3b2(vi) 2y-3y2+4y3
(vii) 5x-4y+3x(viii) 4a-15a2
(ix) xy+yz+zt+tx(x) pqr
(xi) p2q+pq2(xii) 2p+2q

Question 2: Find each of the following products:

5x2 × 4x3-3a2 × 4b4
1/2xy × 2/3x2yz2(-7xy) × (1/4x2yz)
2a(3a + 5b)-11y(3y + 7)
xy (x3 – y3)0.1y (0.1x5 + 0.1y)
4/3a (a2 + b2 – 3c2)1.5x (10x2y – 100xy2)

Question 3: Multiply the monomial by the binomial and find the value of each for x = -1, y = 0.25 and z = 0.005:
(i) 15y2 (2 – 3x)
(ii) -3x (y+ z2)
(iii) z2 (x – y)
(iv) xz (x2 + y2)

Question 4: Simplify:

  • (i) 2x2(x3 – x) – 3x(x4 + 2x) – 2(x4 – 3x2)
  • (ii) x3y(x2 – 2x) + 2xy(x3 – x4)
  • (iii) 3a2 + 2(a+2) – 3a(2a+1)
  • (iv) x(x+4) + 3x(2x2 -1) + 4x2 + 4
  • (v) a(b-c) – b(c-a) – c(a-b)

Question 5: Using the formula for squaring a binomial, evaluate the following:

  • (i) (102)2
  • (ii) (99)2
  • (iii) (1001)2
  • (iv) (999)2
  • (v) (703)2

Frequently Asked Questions On Algebraic Identities For Class 8

Here we have provided some of the frequently asked questions related to the formula of algebraic expression for Class 8.

Q1: Why is Algebra considered important in Mathematics?

A: Algebra is one of the most important branches of Mathematics along with Number Theory, Geometry and Analysis. The concepts of Algebra are crucial to understanding the theory of Partial Differential Equations. Apart from that, algebra is quite important in physical systems such as movement and forces as well as heat transfers, and more.

Q2: What are the different components of the Algebra formulas and expressions?

A: Algebra formulas and expressions can be divided into the following components:
1. Algebraic Identities
2. Laws of Exponent
3. Quadratic Equations
4. Other Important Expressions

Q3: What is the difference between Algebra and Arithmetic?

A: Algebra uses letters to represent values that are either unknown or allowed to take on many values. On the other hand, Arithmetic is all about the computation of specific numbers. Arithmetic consists of simple operations like division, multiplication, addition and subtraction, whereas Algebra is the Math of finding unknown values in an equation with the help of variables.

Q4: What does the word “algebra” mean?

A: The word “algebra” has several related meanings in Mathematics. When used as a single word, it means “a broad part of mathematics”. Algebra can also be used with qualifiers like linear algebra, elementary algebra, modern algebra, etc.

Now that we have provided all the important Algebra formulas, you should take mock tests on this chapter. Embibe provides free Class 8 Algebra Mock Test that will help you in your preparation. It will prove to be helpful in making your journey a rather easy one. Solve the free Class 8 Maths Questions and refer to these formulas when necessary.

If you have any queries, feel free to ask in the comment section below and we will get back to you. Embibe wishes you all the best!

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Methods to Verify Algebraic Identities. (image will be updated soon)

Using Substitution Method.

  • Substitution generally means putting numbers or values in the place of variables or letters.

  • In the substitution method, an arithmetic operation is performed by substituting the values for the variables.

  • For example, when we have x-2=4

When we substitute x= 6, 

On the Right-hand side,

4

On the left hand-side,

x-2 = 6 - 2 = 4

Here, Right hand side = Left hand side which means (x-2) is an identity.

Suppose, (a+3) (a-3) = (a2-9) 

Substituting a= 1

On the Right- hand side,

(a2-9) = (1-9) = -8

On the Left- hand side,

(a+3) (a-3) = (1+3) (1-3) = (4) (-2) = -8

Here, Right hand side = Left hand side which means that (a+3) (a-3) is an identity.

Using Activity Method.

  • In this method, the algebraic identity is verified geometrically by taking different values of a x and y.

  • In the activity method, the identities are verified by cutting and pasting paper.

  • To verify an identity using this method, you need to have a basic knowledge of Geometry.

Identities Class 8 -

The standard identities class 8 are derived from the Binomial Theorem. The table below consists of some Standard identities in maths class 8.

Identity I

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

Identity II

(a-b)2 = a2- 2ab+b2

Identity III

a2-b2= (a+b) (a-b)

Identity IV

(x+a) (x+b) = x2+(a+b) x+ab

Identity V

(a+b+c)2= a2+b2+c2+ 2ab+2bc+2ca

Identity VI

(a+b)3= a3+b3+3ab(a+b)

Identity VII

(a-b)3= a3 -b3-3ab(a-b)

Identity VIII

a3 +b3+c3-3abc

Now, you Might Think What a Binomial Theorem is!

  • In algebra, the Binomial Theorem is defined as a way of expanding a binomial expression raised to a large power which might be troublesome.

  • A polynomial equation with just two terms generally having a plus or a minus sign in between is known as a Binomial expression.

A small Explanation for the Above Algebraic Identities for Class 8.

For example, let us take one of the basic identities,

(a+b)2 = a2+2ab+b2, which holds for all the values of a and b.

  • An identity holds true for all the values of a and b.

  • We can possibly substitute one instance of one side of the equality with its other side.

  • In simple words, (a+b)2 can be replaced by a2+2ab+b2 and vice versa.

  • These can be used as shortcuts which make manipulating algebra easier.

Factoring Identities

The identities listed below in the table are factoring formulas for identities of algebraic expressions class 8.

  x2-y2 =

(x+y) (x-y)

  x3-y3 =

(x-y) (x2+xy+ y2)

  x3 +y3 =

(x+y) (x2 -xy+ y2)

  x4-y4 =

(x2-y2) (x2 +y2)

Three - Variable Identities -

By manipulation of the various discussed identities

entities of algebraic expressions class 8 we get these three- variable identities.

(x+y) (x+z) (y+z) = 

(x+y+z) (xy+yz+xz)-xyz

  x2 +y2+z2          =

(x+y+z)2- 2(xy+yz+xz)

    x3 +y3+z3             =

(x+y+z)(x2 + y2 +z2 -xy-xz-yz)

Important Algebraic Expressions and Identities Class 8 Formula -

The Four Basic Identities in Maths Class 8 have Been Listed Below.

Identity I

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

Identity II

(a-b)2 = a2- 2ab+b2

Identity III

a2-b2= (a+b) (a-b)

Identity IV

(x+a) (x+b) = x2+(a+b) x+ab

Questions to be Solved on Identities Class 8

Question 1) Find the product of (x-1) (x-1)

Solution) We need to find the product (x-1) (x-1),

(x-1) (x-1) can also be written as (x-1)2.

We know the formula for (x-1)2, expand it

(a-b)2 = a2- 2ab+b2 where a= x, b=1

(x-1)2 = x2- 2x+1

Therefore, the product of (x-1) (x-1) is x2- 2x+1 

Question 2) Find the product of (x+1) (x+1) as well as the value of it using x = 2.

Solution) We need to find the product (x+1) (x+1),

(x+1) (x+1) can also be written as (x+1)2.

We know the formula for (x+1)2, expand it

(a+b)2 = a2+ 2ab+b2 where a= x, b=1

(x+1)2 = x2+ 2x+1

Putting the value of x = 2 in equation 1,

(2)2+ 2(2) +1 = 9

Therefore, the product of (x+1) (x+1) is x2+ 2x+1 and the value of the expression is 9.

Question 3) Separate the constants and the variables from the given question.

-4, 4+x, 3x+4y, -5, 4.5y, 3y2+z

Solution) Variables are the ones which include any letter such as x, y, z etc along with the numbers.

In the given question, 

Constants = -4, -5

Variables = 3x+4y, 4+x, 4.5y, 3y2+z

Question 4) Find the value of \[\frac{{{x^2} - 1}}{5}\],at x = -1.

Solution) At x = -1,  \[x = - 1,\frac{{{x^2} - 1}}{5}\]

                                     = \[\frac{{{(-1)^2} - 1}}{5}\]

                                      = 0

Question 5) Find the value of x2+y2 – 10 at x=0 and y=0?

Solution) At x= 0 and y = 0,

x2+y2 – 10 = (0)2+(0)2 – 10 

= -10

Question 6) Solve the following (x+2)2 using the concept of identities.

Solution) According to the identities and algebraic expression class 8,

We know the formula,

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

Where, a= x, b= 2

Let’s expand the given (x+2)2,

Therefore, (x+2)2 = x2+4x+4 is the solution.

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Chapter 9 Class 8 Algebraic Expressions and Identities

Get NCERT Solutions of Chapter 9 Class 8 Algebraic Expressions and Identities free at Teachoo. Answers to all exercise questions, examples have been solved with step-by-step solutions. Concepts are explained before doing the questions.

 

In this chapter, we will learn

  • What are algebra expressions
  • Terms, Factors and Coefficients in an Algebra Expression
  • What are monomials, binomials, trinomials and polynomials
  • What are like and unlike terms in an algebraic expression
  • Adding and Subtracting Algebra Expression
  • Multiplication of Algebra Expressions
    • Multiplying two monomials
    • Multiplying three or more monomials
    • Multiplying Monomial by a Binomial
    • Multiplying Monomial by a Trionmial
    • Multiplying Binomial by a Binomial
    • Multiplying Binomial by a Trionmial
  • Algebra Identities

 

Here, we have divided the chapter into 2 parts - Serial Order Wise and Concept Wise.

Just like the NCERT Book, in Serial Order Wise, the chapter is divided into exercises and examples. This is useful if you are looking for answer to a specific question.

But:

That is not a good way of studying.

In the NCERT Book, first question is of some topic, second question is of some other topic. There is no order

We have solved that using Concept Wise.

In Concept Wise, the chapter is divided into concepts. First the concept is taught. Then the questions of that concept is answered, from easy to difficult.

 

Click on a link to start doing the chapter

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Maths Algebraic Expressions part 1 (Introduction) CBSE Class 8 Mathematics VIII

If you are worried about internet connectivity then don’t worry as  NCERT Solutions Class 8 Maths Chapter 9 are available in pdf format. They are easy to download and after downloading, these solutions can be accessed as per students' wish. These NCERT Solutions Class 8 are available on our website and our app. NCERT Solutions Class 8 is entirely free of cost. So if you are going to have a test or exam near, our NCERT Solutions Class 8 is there for you. These solutions help in the last minute revision of the chapters and ensure that one does not miss the most important questions of NCERT.

NCERT Solutions for Class 8 Maths Chapter 9

Chapter - 9 Algebraic Expressions and Identities

In the curriculum of Class 8 Maths Chapter 9 is Algebraic Expressions and Identities.

Algebra is introduced in Class 8th to make the students know about the algebraic terms, algebraic identities, variables, constants, algebraic expressions, monomial, binomial and trinomial expressions. Also, the mathematical operations like addition, subtraction, multiplication, and division of algebraic expressions are explained in this chapter.

Algebra and its real-life applications are an important part of the maths syllabus. Various Exercises are given in Chapter 9 Maths for students to solve and become familiar with algebra.

With our Grade 8 NCERT solutions, it becomes easy for students to understand the algebraic concepts and solve the questions. These solutions are prepared by our subject experts.

Class 8 Maths Chapter 9 Marks Weightage

Chapter 9 Algebraic Expressions and Identities is a very important chapter from any exam point of view whether it's school exams or competitive exams thus going through these NCERT Solutions will help the student to get a good score on their exams.

In this chapter, a total of 5 Exercises are given with different types of questions and our solutions will help the students to solve these questions.

We Cover all Exercises in the Chapter Given Below:

Exercise 9.1 - 4 Questions with Solutions.

Exercise 9.2 - 5 Questions with Solutions.

Exercise 9.3 - 5 Questions with Solutions.

Exercise 9.4 - 3 Questions with Solutions.

Exercise 9.5 - 8 Questions with solutions.

Why are NCERT Solutions Class 8 Chapter 9 Important?

  • Preparing from our NCERT Solutions Class 8  helps students to gain confidence over the chapter through detailed explanations given in our NCERT solutions.

  • NCERT solutions ensure that students have gone through all the questions given in NCERT which are important from an exam point of view.

  • Last-minute revision and preparation can be easily done by these solutions.

  • NCERT Solutions are made in simple language which makes it understandable for the students.

  • NCERT solutions also give the students an idea of how a mathematical solution must be written.

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Expressions class 8 for algebraic

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Basics of Algebraic Expressions (GMAT/GRE/CAT/Bank PO/SSC CGL) - Don't Memorise

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