#
Parts of an Expression

algebraic expressions are combinations of variables, numbers, and at least one arithmetic process .

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

**
Term:
** Each expression is made up of terms. A term can be a sign total, a variable, or a constant multiplied by a variable or variables.

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**
Factor:
** Something which is multiplied by something else. A factor can be a number, variable, condition, or a longer expression. For model, the construction 7 ten ( y + 3 ) has three factors : 7, ten, and ( y + 3 ) .

**The numeric agent of a multiplication formula that contains a variable. Consider the expression in the figure above, 2 ten + 4 y − 9. In the first gear condition, 2 x, the coefficient is 2 : in the second term, 4 yttrium, the coefficient is 4 .**

Coefficient:

Coefficient:

**A issue that can not change its value. In the construction 2 x + 4 yttrium − 9, the term 9 is a constant .**

Constant:

Constant:

**Terms that contain the same variables such as 2 thousand, 6 m or 3 x yttrium and 7 x y. If an construction has more than one constant terms, those are besides like terms .**

Like Terms:

Like Terms:

expression

Word Phrases

newton + 5

Sum of a number and 5

megabyte − 7

remainder of a numeral and 7

6 ten

merchandise of 6 and a phone number

yttrium ÷ 9

quotient of a act and 9

Example:

Identify the terms, like terms, coefficients, and constants in the formula.

9 m − 5 north + 2 + m − 7

first, we can rewrite the subtractions as additions .

9 meter − 5 north + 2 + megabyte − 7 = 9 m + ( − 5 nitrogen ) + 2 + thousand + ( − 7 )

so, the **
terms
** are 9 m, ( − 5 normality ), m, 2, and ( − 7 ) .

**are terms that contain the same variables .**

Like terms

Like terms

9 m and 9 m are a pair of

**. The changeless terms 2 and − 7 are besides like terms .**

like terms

like terms

**are the numeral parts of a term that contains a variable .**

Coefficients

Coefficients

thus, here the

**are 9, ( − 5 ), and 1. ( 1 is the coefficient of the term megabyte. )**

coefficients

coefficients

The

**terms are the terms with no variables, in this case 2 and − 7 .**

constant

constant

algebraic expressions must be written and interpreted carefully. The algebraic formulation 5 ( x + 9 ) is

**equivalent to the algebraic construction, 5 x + 9 .**

not

not

See the difference between the two expressions in the mesa below .

Word Phrases

Word Phrases

Algebraic Expression

Algebraic Expression

Five times the sum of a number and nine

5 ( ten + 9 )

Nine more than five times a number

5 adam + 9

In writing expressions for stranger quantities, we often use standard formulas. For model, the algebraic expression for “ the distance if the rate is 50 miles per hour and the time is deoxythymidine monophosphate hours ” is D = 50 T ( using the rule D = R T ) .

An expression like x newton is called a power. here x is the establish, and newton is the exponent. The advocate is the number of times the base is used as a factor. The discussion phrase for this expression is “ adam to the normality thorium world power. ”

here are some of the examples of using exponents .

Word Phrases

Algebraic Expression

Seven times

m

to the fourth power

7 megabyte 4

The sum of

x

squared and

12

times of

y

ten 2 + 12 y

x

cubed times

y

to the sixth power

x 3 ⋅ yttrium 6