1. Parts of an Expression
Lesson 6.03

2. After completing this lesson, you will be able to say:
I can identify parts of an expression as a single entity.
I can identify parts of an expression using mathematical terms (sum, difference, product, quotient, factor, coefficient, and term).

3. Algebraic Expressions
Understanding the parts of an algebraic expression is much like putting together puzzle pieces. Each individual piece connects to the next, and together, they create the whole masterpiece.

4. Parts of an Expression Example: 2x2 – 3y – z + 6 Variable:
Expressions, whether they are mathematical or verbal, can contain variables. A variable is a letter that holds the place for some unknown value in an expression.
expressions can have two or more unknown values. In those cases, you simply use a new letter for each unknown value.
the given mathematical expression has three unknown values because there are three variables: x, y, and z
Term:
Expressions are made up of terms separated by a plus or minus sign. Terms can contain variables, numbers, or products of variables and numbers.
The given expression contains four total terms: 2x2, −3y, −z, and 6. Notice how the plus or minus sign is attached to the term immediately following it.

5. Parts of an Expression Example: 2x2 – 3y – z + 6 Factor:
Factors are numbers you multiply together to produce a product.
Look at the factors that are easily seen in the given expression.
2 and x2 are factors of 2x2
−3 and y are factors of −3y
−1 and z are factors of −z
Coefficient:
When multiplying a variable and a number to write a term, the number is listed first and is called the coefficient. It is important to remember the sign in front of the term also goes with that term.
The coefficients in this expression are 2, −3, and −1

6. Parts of an Expression Example: 2x2 – 3y – z + 6 Constant:
Constants are numbers that stand alone. They are called constants because they have fixed value
The constant of this expression is 6

7. Identify the parts of: 4(t + 3) – s
Example
Identify the parts of: 4(t + 3) – s
Variables: t and s
Term: There are two terms in this expression: 4(t + 3) and –s
Factor: Parentheses not only group operations together, they also mean multiplication of two factors. 4 and t + 3 are factors of the term 4(t + 3).
As well, –1 and s are factors of the terms –s
Coefficient: The coefficients in this expression are 4, 1, and –1
Constant: In this expression, the second factor of the term 4(t + 3) has a constant of 3
Remember, if there is no number in front of a variable, it is understood as 1 times that variable and is not written

8. Try it
Identify the variable(s), term(s), factor(s), coefficient(s), and constant(s) in the expression shown below.
4xy − 7x2y + x + 5

9. Check your work

10. Try it
Describe this expression below by identifying parts of the expression using any of the words sum, difference, product, quotient, factor, coefficient, and term.
5x + 13

11. Check your work The variable in this expression is x or some number.
This expression is finding the sum of two terms, 5x and 13, where 5 and x are factors of the product 5x, and 13 is a constant term.
Therefore, a description of this expression can be “a two-term expression that is the sum of five times a number and a constant of 13.”

12. Now that you completed this lesson, you should be able to say:
I can identify parts of an expression as a single entity.
I can identify parts of an expression using mathematical terms (sum, difference, product, quotient, factor, coefficient, and term).