What is an Expression?

An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, *, /) that represents a value. It can contain variables, constants, and mathematical operations. Expressions are used to represent a mathematical relationship or to perform calculations.

Types of Expressions

There are several types of expressions in mathematics:

1. Numerical Expression: A numerical expression contains only numbers and mathematical operations. For example, 3 + 4 * 2 is a numerical expression.
2. Variable Expression: A variable expression contains variables, constants, and mathematical operations. For example, 2x + 5 is a variable expression.
3. Algebraic Expression: An algebraic expression contains variables, constants, and mathematical operations. For example, 3x^2 - 2xy + 7 is an algebraic expression.

Parts of an Expression

An expression is made up of several parts:

• Term: A term is a single mathematical expression separated by + or - signs. For example, in the expression 3x^2 - 2xy + 7, the terms are 3x^2, -2xy, and 7.
• Coefficient: The coefficient is the numerical factor of a term. For example, in the term 5x, the coefficient is 5.
• Variable: A variable is a symbol that represents a value. Common variables include x, y, and z.
• Constant: A constant is a fixed value that does not change. For example, in the expression 2x + 5, the constant is 5.

Simplifying Expressions

To simplify an expression, you perform operations such as combining like terms, distributing, and factoring. Here are some key steps for simplifying expressions:

1. Combine Like Terms: Combine terms with the same variables and exponents. For example, in the expression 3x + 2x - 5x, you can combine 3x and 2x to get 5x.
2. Distribute: Use the distributive property to multiply terms inside parentheses. For example, in the expression 2(3x + 4), you can distribute the 2 to get 6x + 8.
3. Factor: Factor out common terms or use factoring techniques to simplify the expression. For example, in the expression x^2 - 4x, you can factor it as x(x - 4).

Practice Problems

Now that you understand expressions, here are some practice problems to test your knowledge:

1. Simplify the expression 5x + 3 - 2x.
2. Factor the expression x^2 + 5x + 6.
3. Simplify the expression 2(3x - 4) - 5(2x + 1).