Algebraic expressions are combinations the variables , numbers, and at least one arithmetic operation.
for example, 2 x + 4 y − 9 is one algebraic expression.
Term: every expression is consisted of of terms. A term deserve to be a signed number, a variable, or a constant multiplied by a change or variables.
Factor: Something which is multiplied by something else. A element 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 element of a multiplication expression that consists of a variable. Think about the expression in the number above, 2 x + 4 y − 9 . In the very first term, 2 x , the coefficient is 2 : in the second term, 4 y , the coefficient is 4 .
Constant: A number that cannot change its value. In the expression 2 x + 4 y − 9 , the term 9 is a constant.
prefer Terms: Terms that contain the exact same variables such as 2 m , 6 m or 3 x y and also 7 x y . If one expression has an ext than one continuous terms, those are also like terms.
n + 5
sum of a number and also 5
m − 7
distinction of a number and also 7
Product of 6 and a number
y ÷ 9
Quotient the a number and 9
You are watching: Rewrite the expression as an algebraic expression in x.
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 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 ( − 7 ) .
like terms space terms the contain the exact same variables.
9 m and also 9 m space a pair of prefer terms . The consistent terms 2 and also − 7 are also like terms.
Coefficients space the numerical components of a ax that consists of a variable.
So, below the coefficients space 9 , ( − 5 ) , and 1 . ( 1 is the coefficient of the hatchet m .)
The constant terms are the terms with no variables, in this situation 2 and also − 7 .
Algebraic expressions must 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 in between the two expressions in the table below.
|indigenous Phrases||Algebraic Expression|
|five times the amount of a number and nine|| |
5 ( x + 9 )
|Nine more than 5 times a number|| |
5 x + 9
In composing expressions because that unknown quantities, we regularly use traditional formulas. Because that example, the algebraic expression because that "the street if the price is 50 miles per hour and the time is T hours" is D = 50 T (using the formula D = R T ).
one expression like x n is dubbed a power. Here x is the base, and also n is the exponent. The exponent is the variety of times the basic is provided as a factor. The word expression for this expression is " x to the n th power."
right here are several of the examples of making use of exponents.
|native Phrases||Algebraic Expression|
|seven times m come the 4th power|| |
7 m 4
|The sum 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