Algebraic Expressions: Simplifying and Evaluating

What is an Algebraic Expression?

An algebraic expression is a mathematical phrase that combines numbers, variables (letters like x, y, z) and operations (+, -, x, /) without an equals sign. For example, 3x + 5 and 2a - 4b + 7 are algebraic expressions.

Key Terms

• Term: a single number, variable, or numbers and variables multiplied together, e.g. 4x, -7, 2ab.
• Coefficient: the number multiplying a variable, e.g. in 6x, 6 is the coefficient.
• Like terms: terms with exactly the same variable(s) raised to the same power, e.g. 3x and 5x.

Simplifying Expressions

To simplify, collect and combine like terms. Example: 5x + 3x - 2 = 8x - 2. Unlike terms (e.g. 3x and 4y) cannot be combined.

Evaluating Expressions

To evaluate an expression, substitute given values for the variables and carry out the arithmetic. Example: if x = 2, then 3x + 5 = 3(2) + 5 = 11.

Worked Example

Simplify: 4x + 3y - 2x + y = (4x - 2x) + (3y + y) = 2x + 4y.