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

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

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

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

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

prefer Terms: Terms that contain the very same variables such together 2 m , 6 m or 3 x y and also 7 x y . If an expression has an ext than one continuous terms, those are likewise like terms.

Expression

native Phrases

n + 5

amount of a number and 5

m − 7

difference of a number and also 7

6 x

Product the 6 and also a number

y ÷ 9

Quotient that a number and also 9




You are watching: The numerical factor of a term

Example:

identify the terms, favor terms, coefficients, and also constants in the expression.

9 m − 5 n + 2 + m − 7

First, we have the right to rewrite the subtractions as 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 ) .

like terms room terms the contain the exact same variables.

9 m and also 9 m room a pair that choose terms . The consistent terms 2 and also − 7 are likewise like terms.

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

So, right here the coefficients space 9 , ( − 5 ) , and 1 . ( 1 is the coefficient the the ax m .)

The continuous terms room the terms through no variables, in this case 2 and also − 7 .


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

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

word 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 writing expressions for unknown quantities, we regularly use standard formulas. Because that example, the algebraic expression for "the distance if the rate is 50 miles every hour and the time is T hours" is D = 50 T (using the formula D = R T ).

one expression like x n is referred to as a power. Right here x is the base, and also n is the exponent. The exponent is the number of times the base is provided as a factor. The word expression for this expression is " x come the n th power."

here are several of the instances of making use of exponents.

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


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