# NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

NCERT Solutions for Class 8 Maths Chapter 9 can solve all your doubts regarding the chapter. Algebraic Identities might seem easy at first but they are tricky to handle. Similarly, you might get confused on how to multiply two algebraic expressions correctly. Now you can learn everything discussed in this chapter with our NCERT solutions.

CBSE Class 8 Maths Chapter 9 has 5 exercises with 31 questions. Solving these questions will make it much easier for you to practice the topics of the chapter like application of algebraic identities and multiplication of polynomials, binomials and trinomials. We have created stepwise NCERT Solutions for Class 8 so that you do not face any issues in answering the questions in exams.

## NCERT Solution for Class 8 Maths Chapter 9: Algebraic Expressions and Identities – A Brief Explanation

Any expression with constants, variables, which are joint by the operations like addition and subtraction etc. For example- 5x, 7x-8, 3x+2 etc. To understand this Algebraic Expression minutely, it is very much important to comprehend other factors as well especially some of the notable terms related to that. The first is *‘Term’*– It is either a single number or variable or a combination of the numbers and variables together, which is usually separated by the different operators like +,-, etc. Examples of terms are y, 7, 2z, etc.

Other significant terminologies related to this chapter are Factors (product of number and variable, e.g.-7x has two factors that are 7 and x); Coefficient (the number multiplied to a variable, e.g.- In 2x, 2 is the coefficient); Monomials; Binomials; Trinomials; Polynomials; Like and Unlike terms.

Further, the addition and subtraction of the Algebraic expressions form an integral part of NCERT Solutions for Class 8 Maths Chapter 9 – ‘Algebraic Expressions and Identities’. While adding and subtracting Algebraic Expressions, we can only perform the operations for the like terms. For example, while adding 2g+5 and 8+8g, the answer will be 10g+13. Similarly, if we are to subtract 2x+5xy+1 from 7x+2xy+3, the answer will be 5x-3xy+2.

Next topic to be discussed here is the Multiplication of Algebraic Expressions. The two key points to be kept in mind while multiplying the two algebraic expressions is that only the coefficients will be multiplied and the power of the resulting variable will be the addition of the individual powers.

For example, while multiplying 5x and 2x the answer will be 10×2. In the case of the Unlike terms, only the coefficients get multiplied, and if the variables are different then there will be no change in the power of variables. And, if any of the variables are the same then their respective power will be added.

Then the lesson describes what Identities. The formulae in Algebra are called Identity. The identities that will be used in the lesson are as follows:

- (a + b)
^{2}= a^{2}+ b^{2}+2ab - (a – b)
^{2}= a^{2}+ b^{2}– 2ab - (a + b) (a – b) = a
^{2}– b^{2} - (a+ b+ c)
^{2}= a^{2}+ b^{2}+c^{2}+2ab + 2bc + 2ca - (a – b – c)
^{2}= a^{2}+ b^{2}+ c^{2}– 2ab + 2bc -2ca - (a + b)
^{3}= a^{3}+ b^{3}+ 3ab (a + b) - (a – b)
^{3}= a^{3}– b^{3}+ 3ab^{2}– 3a^{2}b

## Discussion on NCERT Solutions for Class 8 Maths Chapter 9 – Algebraic Expressions and Identities

- Exercise 9.1 consists of 4 questions based on your understanding regarding coefficients and Algebraic expressions.
- Exercise 9.2 has 5 questions that will understand your knowledge regarding monomials, binomials, and polynomials.
- Exercise 9.3 comprises 5 questions that are based on addition and subtraction of algebraic expressions. Exercise 9.4 carries 3 questions based on multiplications of Algebraic expressions.
- Exercise 9.5 has 8 questions that will examine your calculation skills regarding identities.

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