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Term: Each expression is made up of terms. A term can be a signed number, a variable, or a constant multiplied by a variable or variables.
Factor: Something which is multiplied by something else. A factor can be a number, variable, term, or a longer expression. For example, the expression 7x(y+3) has three factors: 7 , x , and (y+3) .
Coefficient: The numerical factor of a multiplication expression that contains a variable. Consider the expression in the figure above, 2x+4y−9 . In the first term, 2x , the coefficient is 2 : in the second term, 4y , the coefficient is 4 .
Constant: A number that cannot change its value. In the expression 2x+4y−9 , the term 9 is a constant.
Like Terms: Terms that contain the same variables such as 2m , 6m or 3xy and 7xy . If an expression has more than one constant terms, those are also like terms.
Expression
Word Phrases
n+5
Sum of a number and 5
m−7
Difference of a number and 7
6x
Product of 6 and a number
y÷9
Quotient of a number and 9
Example:
Identify the terms, like terms, coefficients, and constants in the expression.
9m−5n+2+m−7
First, we can rewrite the subtractions as additions.
9m−5n+2+m−7=9m+(−5n)+2+m+(−7)
So, the terms are 9m , (−5n) , m , 2 , and (−7) .
Like terms are terms that contain the same variables.
9m and 9m are a pair of like terms . The constant terms 2 and −7 are also like terms.
Coefficients are the numerical parts of a term that contains a variable.
So, here the coefficients are 9 , (−5) , and 1 . ( 1 is the coefficient of the term m .)
The constant terms are the terms with no variables, in this case 2 and −7 .
Algebraic expressions must be written and interpreted carefully. The algebraic expression 5(x+9) is not equivalent to the algebraic expression, 5x+9 .
See the difference between the two expressions in the table below.
Word Phrases Algebraic Expression
Five times the sum of a number and nine
5(x+9)
Nine more than five times a number
5x+9
In writing expressions for unknown quantities, we often use standard formulas. For example, the algebraic expression for "the distance if the rate is 50 miles per hour and the time is T hours" is D=50T (using the formula D=RT ).
An expression like xn is called a power. Here x is the base, and n is the exponent. The exponent is the number of times the base is used as a factor. The word phrase for this expression is " x to the nth power."
Here are some of the examples of using exponents.
Word Phrases Algebraic Expression
Seven times m to the fourth power
7m4
The sum of x squared and 12 times of y
x2+12y
x cubed times y to the sixth power
x3⋅y6
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Answer:
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