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Mathematics · Class 9 · Chapter 3: Algebraic Expressions and Formulas

8 min

Key points

An algebraic expression is a mathematical phrase that contains variables, constants, and operations
Like terms have the same variables with the same powers and can be combined
Unlike terms cannot be combined as they have different variables or different powers
Addition and subtraction of algebraic expressions is done by combining like terms only
Multiplication of algebraic expressions follows distributive property: a(b+c) = ab + ac
Special products include (a+b)², (a-b)², (a+b)(a-b), and (x+a)(x+b)
Factorization is the reverse process of multiplication where we express an expression as a product of its factors
Common methods of factorization include taking out common factors, grouping, and using algebraic identities
Remainder theorem states that when polynomial f(x) is divided by (x-a), the remainder is f(a)

Definitions

Algebraic Expression: A mathematical phrase that contains one or more variables, constants, and operations like addition, subtraction, multiplication, and division.
Like Terms: Terms that have exactly the same variables with the same powers. Only the coefficients may be different.
Factorization: The process of expressing an algebraic expression as a product of its factors.
Polynomial: An algebraic expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents of variables.

Worked example

Define algebraic expression. Expand and simplify: (2x + 3y)² - (2x - 3y)² (6 marks)

Algebraic expression is a mathematical phrase containing variables, constants, and arithmetic operations. Final answer: 24xy

Common mistakes

Students often combine unlike terms (e.g., adding 3x² + 4x = 7x²)
Forgetting to multiply all terms when using distributive property
Not taking out the complete common factor during factorization
Making sign errors when expanding (a-b)² formula
Confusing coefficient with degree of a term

Quick recap

Algebraic expressions contain variables, constants, and operations. Know the basic identities: (a+b)² = a² + 2ab + b², (a-b)² = a² - 2ab + b², a² - b² = (a+b)(a-b), and (a+b)³ = a³ + 3a²b + 3ab² + b³. Terms are separated by + or - signs, coefficients are numerical parts, and degree is the highest power. Practice factorization and expansion systematically.

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