CHAPTER 8 — ALGEBRAIC EXPRESSIONS (Introduction)

Algebra is a branch of mathematics in which we use letters (like x, y, a, b) to represent numbers.

These letters are called variables.

We combine variables with numbers using operations (+, −, ×, ÷) to form expressions.

A term is a product of numbers and variables.

Examples:

• \(5x\) → a term (5 is coefficient, x is variable)
• \(-3xy\) → a term (−3 is coefficient, x and y are variables)
• \(7\) → a term (only number, called a constant term)

An algebraic expression is formed by combining terms using + or − signs.

Examples:

• \(2x + 3\)
• \(4x^2 - 5x + 7\)
• \(3xy + 5y - 9\)

Based on the number of terms, expressions are classified as:

• Monomial → An expression with one term. Example: \(7x, -3y^2, 5xy\)
• Binomial → An expression with two terms. Example: \(x + y, 3x - 4y\)
• Trinomial → An expression with three terms. Example: \(x^2 + 3x + 2\)
• Polynomial → An expression with one or more terms. Example: \(2x^3 + x^2 - 5x + 7\)

The coefficient of a term is the numerical factor multiplied with the variable(s).

Examples:

• In \(7x\), coefficient = 7
• In \(-3xy\), coefficient = −3
• In \(5x^2y\), coefficient = 5

Like terms are terms that have the same variables raised to the same powers.

Examples:

• \(3x\) and \(7x\) → like terms
• \(4y^2\) and \(-9y^2\) → like terms

Unlike terms have different variables or different powers.

Examples:

• \(2x\) and \(3y\) → unlike terms
• \(x^2\) and \(x^3\) → unlike terms

A constant term is a number without any variable.

Examples: 5, −7, 12 are constants.

• Term = number × variable(s)
• Expression = sum/difference of terms
• Monomial = 1 term, Binomial = 2 terms, Trinomial = 3 terms
• Coefficient = numerical part of term
• Like terms = same variables and powers
• Constant = only number