Algebraic Expressions

Algebraic expressions are the basic units of algebra. An expression consists of numbers (constants), letters (variables), and mathematical operations (addition, subtraction, multiplication, division, exponentiation). They can be very simple or complex.

Basic Concepts

• Constant: a fixed value, such as 5 or -2.
• Variable: a letter representing an unknown or arbitrary value, e.g., x or y.
• Coefficient: the multiplier in front of the variable, e.g., 3 in 3x.
• Term: a part of the expression separated by + or −, e.g., 3x, 5, -2y.

Simple Examples

In this expression, 3x is a variable term where 3 is the coefficient, x is the variable, and 5 is a constant term.

In this expression, there are three terms: 2a², -4a, and 7. In the first term, the variable is raised to a power.

Simplifying Expressions

One of the most important operations in algebra is simplifying expressions. This means combining terms with the same variables or calculating the constants.

Only terms with the same variable raised to the same power can be combined. For example, x² and x cannot be combined.

Distributive Property

The distributive property helps in transforming expressions: a(b + c) = ab + ac. This is a frequently used rule in algebraic operations.

Algebraic Expressions in Everyday Life

• If a chocolate costs x forints and you buy 3, the total price is 3x.
• If a taxi has a base fare of 500 forints and each kilometer costs y forints, the total cost is 500 + y·kilometers.
• If each member of a sports club pays 2000 forints monthly and there are n members, the revenue is 2000n.

Practice Exercise