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

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

*

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 change or variables.

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

Coefficient: The numerical aspect of a multiplication expression that contains a variable. Take into consideration the expression in the number 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.

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

Expression

word Phrases

n + 5

amount of a number and 5

m − 7

distinction of a number and 7

6 x

Product that 6 and also a number

y ÷ 9

Quotient that a number and 9




You are watching: Write a word phrase for the algebraic expression 3x 7

Example:

recognize the terms, choose terms, coefficients, and 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 room 9 m , ( − 5 n ) , m , 2 , and ( − 7 ) .

favor terms space terms the contain the same variables.

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

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

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

The continuous terms are the terms v no variables, in this situation 2 and − 7 .


Algebraic expressions have to be written and also interpreted carefully. The algebraic expression 5 ( x + 9 ) is no identical to the algebraic expression, 5 x + 9 .

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

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

In writing expressions because that unknown quantities, we often use typical formulas. Because that example, the algebraic expression for "the street if the price is 50 miles per hour and also the time is T hours" is D = 50 T (using the formula D = R T ).

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

right here are few of the instances of making use of exponents.

word 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 6th power


See more: Which Of The Following Is An Example Of A Semantic Memory? Semantic Memory

x 3 ⋅ y 6