Algebraic Expressions and Identities – Complete Guide For Class 8 Math Chapter 9

Our learning resources for the chapter, Algebraic Expressions and Identities in Mathematics Class 8th chapter 8 are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples.

This chapter introduces algebraic expressions, combining constants and variables. It covers addition, subtraction, multiplication, and factorization of expressions. Students learn to simplify expressions and understand identities like (a+b)² = a²+2ab+b². This foundation aids in solving equations and real-life problems.

Algebraic Expressions and Identities form a crucial part of Class 8 Mathematics, covering fundamental concepts that lay the groundwork for advanced algebra. This chapter delves into expressions, terms, coefficients, and identities, offering a comprehensive understanding of how to manipulate and simplify algebraic expressions.

Expressions

For learning Algebraic Expressions and Identities in class 8 we need to learn first what are expressions.

In algebra, we use letters (variables) and numbers (constants) to represent values. These variables can take various values and when combined with constants using arithmetic operations, they form algebraic expressions. Examples include:

• 5x + 2
• 3 + 2a
• a + b

Expressions can change their values depending on the values assigned to their variables. For instance:

• For x = 1 and y = 1, the expression xy + 2 equals 3.
• For x = 100 and y = 2, the expression xy + 2 equals 202.

Terms and Factors

An algebraic expression comprises terms, which are individual components separated by addition or subtraction. Terms themselves can be formed by multiplying constants and variables, known as factors. For example:

• In the expression 2a + 4ab + 5a(b + c), the terms are 2a, 4ab, and 5a(b + c).
• The factors for these terms are 2 and a; 4, a and b; 5, a and (b + c), respectively.

Coefficients

The numerical part of a term is called its coefficient. For example:

• In the term 5x, the coefficient is 5.
• In the term xy, the coefficient is 1.
• In the term 4z, the coefficient is 4.

Types of Algebraic Expressions

Algebraic expressions can be classified based on the number of terms:

• Monomial: An expression with a single term (e.g., 2x, 3xy, –9z).
• Binomial: An expression with two terms (e.g., 2x + y, 3xy – 4).
• Trinomial: An expression with three terms (e.g., 2x + y + 3z, a – b + c).
• Polynomial: An expression with one or more terms where variables have non-negative exponents (e.g., x + y + z, 17 xyz – 17).

Like and Unlike Terms

Terms with the same variables are called like terms and can be combined. Those with different variables are called unlike terms.

Operations on Algebraic Expressions

Addition

To add algebraic expressions, align the like terms and then sum them. For example:

• Add -8x² + 2y²z – 11 and -2x² + 9y²z – 1:
  • (3+2)x² + (2+9)y²z + (−9+3) = 5x² + 11y²z – 6

Subtraction

Similar to addition, but subtract the corresponding terms:

• Subtract 2x² + 9y²z from 5x² + 11y²z – 6:
  • (5−2)x² + (11−9)y²z + (−6−3) = 3x² + 2y²z – 9

Multiplication

• Monomial × Monomial: Multiply the coefficients and then the variables.
  • 8ab² × 2c = 16ab²c
  • 13a²b × 9abc = 117a³b²c
• Monomial × Polynomial: Use the distributive property to expand the product.
  • xy²z(x + z) = x²y²z + xy²z²
• Polynomial × Polynomial: Each term in one polynomial multiplies each term in the other.

Identities

In chapter 8 of class 8, Algebraic Expressions and Identities we have learned about Algebraic Expressions, and now we will learn about Identities.

Identities are equations that hold for all values of the variables. Important standard identities include:

• (a+b)² = a² + 2ab + b²
• (a−b)² = a² – 2ab + b²
• (a+b)(a−b) = a² – b²
• (x+a)(x+b) = x² + (a + b)x + ab

Applying Identities

Identities simplify calculations in algebraic expressions, especially useful in squaring numbers or finding products quickly.

This chapter builds a strong foundation in algebra, crucial for tackling more complex mathematical problems in future studies. Understanding these concepts enables students to solve equations, factorize expressions, and work with polynomials, laying the groundwork for advanced algebraic techniques.