Expression

An algebraic expression is a set of numbers, variables, and operations (like addition, subtraction, multiplication, and division) combined together to represent a value.

The most important thing to remember is that it does not contain an equals sign or an inequality sign.

Examples of expressions

• 3x + 5
• 2a^2 - 4b + 7
• \frac{1}{2}mv^2 + 3

Non-examples of expressions

• x = 5 (this is an equation, not an expression)
• y > 10 (this is an inequality, not an expression)
• 4 \times (this is incomplete and not a valid expression)

Terms

A term is a single number or variable, or numbers and variables multiplied together. They’re separated by addition or subtraction signs.

For example, in the expression 3x^2 + 5y - 7, there are three terms:

• 3x^2
• 5y
• -7

Coefficients

A coefficient is the *constant& part of a term that multiplies a variable.

For example, in the term 4x^3, the coefficient is 4, meaning that x^3 is multiplied by 4.

Constants

A constant is a term that does not contain any variables. It is simply a fixed number.

For example, in the expression 2x + 3, the constant is 3.

Example problems

Apples weigh a mass of a and bananas weigh a mass of b. Write an expression for the total mass of 3 apples and 4 bananas.

• The mass of 3 apples is 3\cdot a=3a.
• The mass of 4 bananas is 4\cdot b=4b.
• 3a + 4b represents the total mass of 3 apples and 4 bananas.