Algebraic expressions room combinations that variables , numbers, and also 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 made up 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 beg your pardon is multiply by other 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 aspect of a multiplication expression that contains a variable. Consider the expression in the number above, 2 x + 4 y − 9 . In the 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 term 9 is a constant.

like Terms: Terms the contain the exact same variables such as 2 m , 6 m or 3 x y and 7 x y . If an expression has an ext than one consistent terms, those are additionally like terms.

Expression

native Phrases

n + 5

sum of a number and also 5

m − 7

difference of a number and also 7

6 x

Product that 6 and a number

y ÷ 9

Quotient the a number and 9




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Example:

recognize the terms, choose terms, coefficients, and also 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 ) .

favor terms space terms that contain the same variables.

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

Coefficients space the numerical parts of a hatchet that consists of a variable.

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

The consistent terms room the terms through no variables, in this situation 2 and − 7 .


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

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

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

In creating expressions for unknown quantities, we frequently use traditional formulas. Because that example, the algebraic expression because that "the distance 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 referred to as a power. Right here x is the base, and also n is the exponent. The exponent is the variety of times the base is offered as a factor. The word expression for this expression is " x come the n th power."

here are several of the examples of utilizing exponents.

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


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x 3 ⋅ y 6