CBSE NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.1 Algebraic Expressions and Identities in Hindi and English Medium updated for new session 2023-24. The question answers of ex. 8.1 class 8th mathematics are revised according to new syllabus and latest NCERT textbooks issued for CBSE 2023-24.
|Chapter: 8||Exercise: 8.1|
|Chapter Name:||Algebraic Expressions and Identities|
|Medium:||Hindi and English Medium|
|Academic Session:||CBSE 2023-24|
|Content:||NCERT Exercise Solutions|
Class 8 Maths Chapter 8 Exercise 8.1 Solution
Class VIII Mathematics Ex. 8.1 Algebraic Expressions and Identities in Hindi Medium and English Medium free. All the contents are updated according to CBSE syllabus 2023-24. PDF and Videos are given here to explain all the question answers with solution of exercise 8.1 of grade 8 mathematics. Algebraic expression is one of the important chapters of class 8 mathematics.
Algebraic expression is a combination of variables and constant terms, which are connected by mathematical operations of addition, subtraction, multiplication and division”. Consider 2x + 3 and 5a – 2.
(i) 2 and 2 are constants and x is a variable. 2x + 3 is an algebraic expression consisting of two terms 2x and 3 connected together with the sign of addition.
(ii) 5a – 2 consists of two terms 5a and 2, connected together with the sign of subtraction. 5 and –2 are constants whereas a is a variable.
An algebraic expression which has only one term is called a monomial. 2 2 e.g., 2x, 3x y, –5xy etc.
An algebraic expression which has two terms is called a binomial. e.g., 2x + 3, 5x(3/2), 7x + ½ etc.
Any algebraic expression, which has one or more terms is called a trinomial.
5x + y – 6, x² + 5x – 6, x³ – xyz + 7 etc.
Any algebraic expression, which has one or more terms is called a polynomial.
Like and Unlike Terms
In a given expression, the terms having the same literal factors are called like terms, otherwise they are called unlike terms. Consider the algebraic expressions:
(a) 3x² – 7x + 5x² + 2, (b) 4x² – y² + 3x² + 5y² + z, (c) 2xy² – 3x² + 7xy
- (a) 3x² and 5x² are like terms.
- (b) 4x² and 3x² are like terms, – y² and 5y² are like terms.
- (c) There are three terms 2xy², –3x² and 7xy and they are all unlike terms as they have different variables viz. xy², x², xy.
Add: 6a + 8b – 5c, 2b + c – 4a and a – 3b – 2c.
Writing the terms of the given expressions in the same order in form of rows with like terms below each other and adding column wise, we get:
6a + 8b – 5c
– (4a + 2b + c)
+ a – 3b – 2c
= 3a + 7b 6c
What do you learn about algebraic expressions in exercise 8.1 of class 8 Maths?
Class 8 Maths exercise 8.1 explains about the Algebraic expressions in simple way. According to this, algebraic expressions are expressions formed from the variables and the constants. A variable can take any value. The value of an expression changes with the value chosen for variables it contains. A number line has infinite number of points.
What are the main methods in exercise 8.1 of 8th Maths to simplify expressions?
To simplify any algebraic expression, the following are the basic rules and steps are given in class 8 Maths exercise 8.1:
- Remove any grouping symbol such as brackets and parentheses by multiplying factors.
- Use the exponent rule to remove grouping if the terms are containing exponents.
- Combine the like terms by addition or subtraction.
- Combine the constants.
What are the different algeraic methods of addition in class 8 Maths exercise 8.1?
Add: 5x² + 3x – 8, 4x + 7 – 2x² and 6 – 5x + 4x².
Writing the given expressions in descending powers of x in the form of rows with like terms below each other and adding column wise, we get:
5x² + 3x – 8
– 2x² + 4x + 7
4x² – 5x + 6
= 7x² + 2x + 5