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

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

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Term: every expression is consisted of of terms. A term have the right to be a signed number, a variable, or a consistent multiplied by a variable or variables.

Factor: Something i m sorry is multiply by miscellaneous else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7 x ( y + 3 ) has actually three factors: 7 , x , and ( y + 3 ) .

Coefficient: The numerical element of a multiplication expression that includes a variable. Consider the expression in the number above, 2 x + 4 y − 9 . In the very first term, 2 x , the coefficient is 2 : in the 2nd term, 4 y , the coefficient is 4 .

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

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

Expression

native Phrases

n + 5

sum of a number and 5

m − 7

distinction of a number and also 7

6 x

Product the 6 and also a number

y ÷ 9

Quotient of a number and also 9




You are watching: A combination of operations on variables and numbers is called

Example:

determine the terms, choose terms, coefficients, and constants in the expression.

9 m − 5 n + 2 + m − 7

First, we deserve to rewrite the subtractions together additions.

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

So, the state space 9 m , ( − 5 n ) , m , 2 , and ( − 7 ) .

prefer terms room terms that contain the same variables.

9 m and 9 m are a pair that like terms . The continuous terms 2 and − 7 are also like terms.

Coefficients room the numerical components of a term that contains a variable.

So, below the coefficients room 9 , ( − 5 ) , and 1 . ( 1 is the coefficient the the ax m .)

The continuous terms room the terms with no variables, in this instance 2 and − 7 .


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

check out the difference between the 2 expressions in the table below.

native Phrases Algebraic Expression
five times the amount of a number and also nine
5 ( x + 9 )
Nine an ext than five times a number
5 x + 9

In composing expressions because that unknown quantities, we regularly use conventional formulas. For example, the algebraic expression because that "the street if the rate is 50 miles every hour and also the time is T hours" is D = 50 T (using the formula D = R T ).

an expression favor x n is dubbed a power. Below x is the base, and n is the exponent. The exponent is the variety of times the base is supplied as a factor. The word expression for this expression is " x come the n th power."

below are few of the instances of utilizing exponents.

native Phrases Algebraic Expression
seven times m come the 4th power
7 m 4
The sum of x squared and 12 time of y
x 2 + 12 y
x cubed times y to the sixth power


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x 3 ⋅ y 6