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

For example, 2 x + 4 y − 9 is an algebraic expression.

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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 expressi~ above 7 x ( y + 3 ) has three factors: 7 , x , and also ( y + 3 ) .

Coefficient: The numerical factor of a multiplication expression that contains a variable. Consider the expression in the figure above, 2 x + 4 y − 9 . In the first term, 2 x , the coefficient ins 2 : in the second term, 4 y , the coefficient is 4 .

Constant: A number that cannot change its value. In the expressitop top 2 x + 4 y − 9 , the hatchet 9 is a constant.

Like Terms: Terms that contain the same variables such as 2 m , 6 m or 3 x y and 7 x y . If an expression has more than one constant terms, those are also like terms.

Expression

Word Phrases

n + 5

Sum of a number and also 5

m − 7

Difference of a number and 7

6 x

Product of 6 and a number

y ÷ 9

Quotient of a number and 9




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Example:

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

9 m − 5 n + 2 + m − 7

First, we can rewrite the subtractions as additions.

9 m − 5 n + 2 + m − 7 = 9 m + ( − 5 n ) + 2 + m + ( − 7 )

So, the terms are 9 m , ( − 5 n ) , m , 2 , and ( − 7 ) .

Like terms are terms that contain the same variables.

9 m and also 9 m are a pair of like terms . The constant state 2 and also − 7 are also like terms.

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

So, here the coefficients are 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the hatchet m .)

The constant terms are the terms with no variables, in this situation 2 and also − 7 .


Algebraic expressions must be written and interpreted carefully. The algebraic expression 5 ( x + 9 ) is not equivalent to the algebraic expression, 5 x + 9 .

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

Word Phrases Algebraic Expression
Five times the sum of a number and nine
5 ( x + 9 )
Nine more than five times a number
5 x + 9

In writing expressions for unknown quantities, we often use standard formulas. For example, the algebraic expression for "the distance if the rate ins 50 miles per hour and the time is T hours" ins D = 50 T (using the formula D = R T ).

An expression favor x n is called a power. Here x is the base, and n is the exponent. The exponent is the number of times the base is used as a factor. The word phrase for this expression is " x to the n th power."

Here are some of the examples of using exponents.

Word Phrases Algebraic Expression
Seven times m to the fourth power
7 m 4
The sum the x squared and 12 times of y
x 2 + 12 y
x cubed time y to the sixth power


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x 3 ⋅ y 6