GENERAL MATHEMATICS (WAEC FOCUS)

Algebraic Expressions

Introduction Algebra is a part of mathematics where letters are used together with numbers and operation signs. For example, 2x + 3y, ½a² + ¾bc, and 2x² − 3x + 2 are called algebraic expressions. They are made up of numbers, letters, and signs such as +, −, ×, and ÷. In algebra, letters are used to stand for numbers. Some letters can have different values depending on the question. These letters are called variables. For example, in ⅓πr²h, the letters r and h are variables because their values can change. Some values do not change. These are called constants. In the expression ⅓πr²h, ⅓ and π are constants because their values remain fixed. An algebraic expression is divided into smaller parts called terms. Terms are separated by plus (+) or minus (−) signs. For example, in the expression: 3xy² + 2xz³ − 4y + 5 the terms are 3xy², 2xz³, −4y, and +5. A number that appears alone, without any letter attached to it, is called the constant term. In 3xy² + 2xz³ − 4y + 5, the constant term is 5. The number written before a letter or a group of letters is called the coefficient. For example, in 2x − 3x² + 4y³, the coefficient of x is 2, the coefficient of x² is −3, and the coefficient of y³ is 4. Some terms have the same letters raised to the same powers. These are called like terms. For example, 4x²y and 7x²y are like terms because both contain x²y. However, 5x²y and 9xy² are not like terms because the powers of x and y are different. Important Points to Remember In algebra, the multiplication sign × is usually not written. For example, instead of writing a × b, we simply write ab. This also helps us avoid confusing the multiplication sign × with the letter x. In the same way, a ÷ b can be written as a/b. When writing algebraic terms, the number normally comes first, followed by the letters in alphabetical order. For example, 6x²yz and 9abc³ are written in the correct order. The plus (+) or minus (−) sign belongs to the term that comes immediately after it. For example, in 3xy² + 2xz³ − 4y + 5, the term involving 4y is −4y, not just 4y.