Parts of an Expression

Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.

For example, is an algebraic expression.

Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.

Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression has three factors: , , and .

Coefficient: The numerical factor of a multiplication expression that contains a variable. Consider the expression in the figure above, . In the first term, , the coefficient is : in the second term, , the coefficient is .

Constant: A number that cannot change its value. In the expression , the term is a constant.

Like Terms: Terms that contain the same variables such as , or and . If an expression has more than one constant terms, those are also like terms.

Example:

Identify the terms, like terms, coefficients, and constants in the expression.

First, we can rewrite the subtractions as additions.

So, the terms are , , , , and .

Like terms are terms that contain the same variables.

and are a pair of like terms . The constant terms and are also like terms.

Coefficients are the numerical parts of a term that contains a variable.

So, here the coefficients are , , and . ( is the coefficient of the term .)

The constant terms are the terms with no variables, in this case and .

Algebraic expressions must be written and interpreted carefully. The algebraic expression is not equivalent to the algebraic expression, .

See the difference between the two expressions in the table below.

Word Phrases Algebraic Expression
Five times the sum of a number and nine
Nine more than five times a number

In writing expressions for unknown quantities, we often use standard formulas. For example, the algebraic expression for “the distance if the rate is miles per hour and the time is hours” is (using the formula ).

An expression like is called a power. Here is the base, and is the exponent. The exponent is the number of times the base is used as a factor. The word phrase for this expression is ” to the power.”

Here are some of the examples of using exponents.

Word Phrases Algebraic Expression
Seven times to the fourth power
The sum of squared and times of
cubed times to the sixth power

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