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Algebraic expressions are made up of terms. A term is a constant, or the product of a constant and one or more variables.
A term is a constant, or the product of a constant and one or more variables.
Examples of terms are $7,y,5{x}^{2},9a,\text{and}\phantom{\rule{0.2em}{0ex}}{b}^{5}.$
The constant that multiplies the variable is called the coefficient .
The coefficient of a term is the constant that multiplies the variable in a term.
Think of the coefficient as the number in front of the variable. The coefficient of the term 3 x is 3. When we write x , the coefficient is 1, since $x=1\xb7x.$
Identify the coefficient of each term: ⓐ 14 y ⓑ $15{x}^{2}$ ⓒ a .
ⓐ The coefficient of 14
y is 14.
ⓑ The coefficient of
$15{x}^{2}$ is 15.
ⓒ The coefficient of
a is 1 since
$a=1\phantom{\rule{0.2em}{0ex}}a.$
Identify the coefficient of each term: ⓐ $17x$ ⓑ $41{b}^{2}$ ⓒ z .
ⓐ 14 ⓑ 41 ⓒ 1
Identify the coefficient of each term: ⓐ 9 p ⓑ $13{a}^{3}$ ⓒ ${y}^{3}.$
ⓐ 9 ⓑ 13 ⓒ 1
Some terms share common traits. Look at the following 6 terms. Which ones seem to have traits in common?
The 7 and the 4 are both constant terms.
The 5x and the 3 x are both terms with x .
The ${n}^{2}$ and the $9{n}^{2}$ are both terms with ${n}^{2}.$
When two terms are constants or have the same variable and exponent, we say they are like terms .
Terms that are either constants or have the same variables raised to the same powers are called like terms .
Identify the like terms: ${y}^{3},$ $7{x}^{2},$ 14, 23, $4{y}^{3},$ 9 x , $5{x}^{2}.$
${y}^{3}$ and $4{y}^{3}$ are like terms because both have ${y}^{3};$ the variable and the exponent match.
$7{x}^{2}$ and $5{x}^{2}$ are like terms because both have ${x}^{2};$ the variable and the exponent match.
14 and 23 are like terms because both are constants.
There is no other term like 9 x .
Identify the like terms: $9,$ $2{x}^{3},$ ${y}^{2},$ $8{x}^{3},$ $15,$ $9y,$ $11{y}^{2}.$
9 and 15, ${y}^{2}$ and $11{y}^{2},$ $2{x}^{3}$ and $8{x}^{3}$
Identify the like terms: $4{x}^{3},$ $8{x}^{2},$ 19, $3{x}^{2},$ 24, $6{x}^{3}.$
19 and 24, $8{x}^{2}$ and $3{x}^{2},$ $4{x}^{3}$ and $6{x}^{3}$
Adding or subtracting terms forms an expression. In the expression $2{x}^{2}+3x+8,$ from [link] , the three terms are $2{x}^{2},3x,$ and 8.
Identify the terms in each expression.
ⓐ The terms of
$9{x}^{2}+7x+12$ are
$9{x}^{2},$ 7
x , and 12.
ⓑ The terms of
$8x+3y$ are 8
x and 3
y .
Identify the terms in the expression $4{x}^{2}+5x+17.$
$4{x}^{2},5x,17$
If there are like terms in an expression, you can simplify the expression by combining the like terms. What do you think $4x+7x+x$ would simplify to? If you thought 12 x , you would be right!
Add the coefficients and keep the same variable. It doesn’t matter what x is—if you have 4 of something and add 7 more of the same thing and then add 1 more, the result is 12 of them. For example, 4 oranges plus 7 oranges plus 1 orange is 12 oranges. We will discuss the mathematical properties behind this later.
Simplify: $4x+7x+x.$
Add the coefficients. 12 x
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