Algebraic expressions are combicountries of variables , numbers, and also at least one arithmetic operation.

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

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Term: Each expression is comprised 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 which is multiplied by something else. A aspect have the right to be a number, variable, term, or a longer expression. For instance, the expression 7 x ( y + 3 ) has actually 3 factors: 7 , x , and ( y + 3 ) .

Coefficient: The numerical aspect 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 coreliable is 2 : in the second term, 4 y , the coefficient is 4 .

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

Like Terms: Terms that contain the very same variables such as 2 m , 6 m or 3 x y and 7 x y . If an expression has actually more than one consistent terms, those are also like terms.

Expression

Word Phrases

n + 5

Sum of a number and also 5

m − 7

Difference of a number and also 7

6 x

Product of 6 and also a number

y ÷ 9

Quotient of a number and also 9




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Example:

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

9 m − 5 n + 2 + m − 7

First, we can recompose 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 ) .

Like terms are terms that contain the exact same variables.

9 m and 9 m are a pair of like terms . The constant terms 2 and − 7 are likewise choose terms.

Coefficients are the numerical parts of a term that has a variable.

So, right here the coefficients are 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the term m .)

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


Algebraic expressions need to be created and taken closely. The algebraic expression 5 ( x + 9 ) is not identical to the algebraic expression, 5 x + 9 .

See the distinction between the 2 expressions in the table below.

Word Phrases Algebraic Expression
Five times the sum of a number and nine
5 ( x + 9 )
Nine even more than five times a number
5 x + 9

In creating expressions for unknown amounts, we regularly use conventional formulas. For example, the algebraic expression for "the distance if the price is 50 miles per hour and also the moment is T hours" is D = 50 T (making use of the formula D = R T ).

An expression prefer x n is called a power. Here x is the base, and n is the exponent. The exponent is the number of times the base is offered as a factor. The word expression for this expression is " x to the n th power."

Here are some of the examples of making use of exponents.

Word Phrases Algebraic Expression
Seven times m to the fourth power
7 m 4
The amount of x squared and 12 times of y
x 2 + 12 y
x cubed times y to the 6th power


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x 3 ⋅ y 6