RD Sharma Class 8 Solutions Chapter 6 - Algebraic Expressions and Identities (Ex 6.5) Exercise 6.5

Algebraic Expressions and Identities is the Sixth Chapter of RD Sharma Class 8 Math in which students learn about various expressions made up of variables and constants and algebraic operations like addition, subtraction, multiplication, and division. Let us take a look at some algebraic expressions

1. 7x+2

2. 2+3x

3. \[\frac{1}{x} + 2\]

4. \[3x^{2} + \frac{1}{2y}\]

Students will learn about three expressions in the chapter Algebraic Expressions which are numbers, variables, and arithmetic operations. The students learn about six different types of algebraic expressions which are monomial, polynomial, binomial, trinomial, and multinomial. 

Sections of RD Sharma

Sections of RD Sharma Class 8 Math Chapter 6- Algebraic Expressions and Identities:

1. What are Expressions

2. Terms, Coefficient, and Factors

3. Monomials, Binomials, and Polynomials

4. Addition and Subtraction of Algebraic Expressions

5. Like and Unlike Terms

6. Multiplication of Algebraic Expressions

7. Identity

8. Standard Identities

9. Applying Identities

List of Exercises in RD Sharma Class 8 Math Chapter 6- Algebraic Expressions and Identities

Some Important Terms in RD Sharma Class 8 Math Chapter 6- Algebraic Expressions and Identities

1. Terms- A term can be defined as a single mathematical operation. It can be a number or a variable that can be multiplied but never added or subtracted. For example- 2a and 8

2. Factors- A factor in an algebraic expression that divides another number or expression with no remainder. For example-\[\frac{3}{2a}\]

3. Coefficient- A coefficient can be described as a number that is multiplied by a variable. For example- 7q

4. Variables- A variable is an alphabet that can be used to define an unknown identity. For example- x

5. Operations- A mathematical operation can be used to add, subtract, multiply or divide any two expressions.

6. Monomial- A monomial is a term that represents only one term. For example- 2ab

7. Binomial- A binomial is a term that represents two terms, and both cannot be zero. For example-\[a^{2} + b^{2}\]

8. Polynomial- A polynomial is a term that represents more than two terms that are combined by mathematical operations such as addition, subtraction, multiplication but not division.

9. Identity- An identity is an equation which regardless of the value that is assigned to the variables, is always true.

Important Formulas to learn in RD Sharma Class 8 Math Chapter 6- Algebraic Expressions and Identities

1. (a + b)² = a² + b² + 2ab

2. (a - b)² = a² + b² - 2ab

3. a² - b² = (a + b)(a - b)

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

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

6. (a + b)³ = a³ + b³ + 3ab(a + b)

7. (a - b)³ = a³ - b³ - 3ab(a - b)

8. a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² +c² - ab - bc - ca)