How to Identify the Parts of an Algebraic Expression

An algebraic expression is a combination of variables, constants, and algebraic operations (such as addition, subtraction, multiplication, division, and exponentiation with rational exponents).

The following diagrams give two examples of algebraic expressions that shows the parts of the expressions. Scroll down the page for more examples.

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Key difference from equations:

• Expressions don’t have an “=” sign (e.g., 3x + 2)
• Equations do (e.g., 3x + 2 = 8).

Parts of an expression (terms, coefficients and variables) and evaluating expressions
What is a term?
A term is any coefficient and it’s variable.
Examples:

1. Identify the terms in the expression 4x - 2y + 5
   
2. Identify the coefficient and variable in the term.
   
3. Evaluate an expression.
   
4. If x = 4 and y = 2 evaluate 3x + 5y
   
5. Evaluate the expression 3 + a - 2b if a = 7 and b = 2.
   
6. Jim and Jane like to go running in the morning. Jim runs twice as far as Jane. What is the combined distance they travel? Let J be the distance Jane runs.
   

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Vocabulary for Algebraic Expressions
In an algebraic expression, terms are things that are separated by either a + or -.
The official definition is: A term is a number, a variable, or a product or quotient of numbers and variables raised to powers.

Example:
Identify the terms in the following expression:
2x⁴ + 3x³ - 5x² - 8x + 12

Each of the terms is made up of a coefficient and a variable. The coefficient is the number in front of the variable
Example:

1. Name the coefficient in the term 2x⁴
   
2. Name the coefficient in the term x
   
3. Name the coefficient in the term -x
   
   When we just have a number, we call that a constant.
   Example:
   Name the constant in the following expression.
   2x⁴ + 3x³ - 5x² - 8x + 12
   
   When an algebraic expression is written properly, we call it descending order.
   The first term is called the leading term and the number in front of the variable is called the leading coefficient.
   

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Variables and Algebraic
Variable is a symbol, usually a letter, that represents one or more numbers.
Algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols.
Examples:

1. Write an algebraic expression for each phrase
   a) the sum of n and 8
   b) t minus 15
   
   
2. Define a variable and write an algebraic expression for each phrase.
   a) ten more than twice a number
   b) three times a number minus 6
   c) 9 less than a number
   d) the sum of twice a number and 31
   
   An equation is a mathematical sentence that uses an equal sign.
   An open sentence is an equation that contains one or more variables.
   Example:
   
3. Write an equation to show the total incomes from selling tickets to a school play for $5 each.
   
4. Write an equation for the data in the table.
   

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How to Identify Parts of an Expression?
Example:
Identify the terms, like terms, coefficients, and constants in the expression
8m - 6m - 4 + m -7.

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