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

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

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Term: every expression is comprised of terms. A term deserve to be a signed number, a variable, or a constant multiplied by a variable or variables.

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

Coefficient: The numerical element of a multiplication expression that consists of 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 adjust its value. In the expression 2 x + 4 y − 9 , the ax 9 is a constant.

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

Expression

word Phrases

n + 5

amount of a number and 5

m − 7

difference of a number and also 7

6 x

Product of 6 and also a number

y ÷ 9

Quotient that a number and also 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 have the right to rewrite the subtractions together additions.

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

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

prefer terms space terms the contain the same variables.

9 m and 9 m space a pair that prefer terms . The consistent terms 2 and − 7 are also like terms.

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

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

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


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

see the difference between the 2 expressions in the table below.

indigenous Phrases Algebraic Expression
5 times the amount of a number and also 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. Because that example, the algebraic expression because that "the distance if the price is 50 miles every hour and also the time is T hours" is D = 50 T (using the formula D = R T ).

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

right here are some of the examples of using exponents.

native Phrases Algebraic Expression
seven times m to the 4th power
7 m 4
The amount of x squared and also 12 times of y
x 2 + 12 y
x cubed time y come the 6th power


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x 3 ⋅ y 6