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 .
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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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 .
A issue that can not change its value. In the construction 2 x + 4 yttrium − 9, the term 9 is a 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 .
newton + 5
Sum of a number and 5
megabyte − 7
remainder of a numeral and 7
merchandise of 6 and a phone number
yttrium ÷ 9
quotient of a act and 9
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 )
are 9 m, ( − 5 normality ), m, 2, and ( − 7 ) .
are terms that contain the same variables .
9 m and 9 m are a pair of
. The changeless terms 2 and − 7 are besides like terms .
are the numeral parts of a term that contains a variable .
thus, here the
are 9, ( − 5 ), and 1. ( 1 is the coefficient of the term megabyte. )
terms are the terms with no variables, in this case 2 and − 7 .
algebraic expressions must be written and interpreted carefully. The algebraic formulation 5 ( x + 9 ) is
equivalent to the algebraic construction, 5 x + 9 .
See the difference between the two expressions in the mesa below .
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 .
to the fourth power
7 megabyte 4
The sum of
ten 2 + 12 y
to the sixth power
x 3 ⋅ yttrium 6