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$x+4$ is an expression.
$7y$ is an expression.
$\frac{x-3{x}^{2}y}{7+9x}$ is an expression.
The number 8 is an expression. 8 can be written with explicit signs of operation by writing it as $8+0$ or $8\cdot 1$ .
$3{x}^{2}+6=4x-1$ is not an expression, it is an equation . We will study equations in the next section.
In some expressions it will appear that terms are joined by $"-"$ signs. We must keep in mind that subtraction is addition of the negative, that is, $a-b=a+(-b)$ .
An important concept that all students of algebra must be aware of is the difference between terms and factors .
Terms are parts of
sums and are therefore joined by addition (or subtraction) signs.
Factors are parts of
products and are therefore joined by multiplication signs.
Identify the terms in the following expressions.
$3{x}^{4}+6{x}^{2}+5x+8$ .
This expression has four terms: $3{x}^{4},6{x}^{2},\text{\hspace{0.17em}}5x,$ and 8.
$15{y}^{8}$ .
In this expression there is only one term. The term is $15{y}^{8}$ .
$14{x}^{5}y+{(a+3)}^{2}$ .
In this expression there are two terms: the terms are $14{x}^{5}y$ and ${(a+3)}^{2}$ . Notice that the term ${(a+3)}^{2}$ is itself composed of two like factors, each of which is composed of the two terms, $a$ and 3.
${m}^{3}-3$ .
Using our definition of subtraction, this expression can be written in the form ${m}^{3}+(-3)$ . Now we can see that the terms are ${m}^{3}$ and $-3$ .
Rather than rewriting the expression when a subtraction occurs, we can identify terms more quickly by associating the $+$ or $-$ sign with the individual quantity.
${p}^{4}-7{p}^{3}-2p-11$ .
Associating the sign with the individual quantities we see that the terms of this expression are ${p}^{4},\text{\hspace{0.17em}}-7{p}^{3},\text{\hspace{0.17em}}-2p,$ and $-11$ .
Let’s say it again. The difference between terms and factors is that terms are joined by
addition, multiplication
List the terms in the following expressions.
$4{x}^{2}-8x+7$
$4{x}^{2},\text{\hspace{0.17em}}-8x,\text{\hspace{0.17em}}7$
$2xy+6{x}^{2}+{(x-y)}^{4}$
$2xy,\text{\hspace{0.17em}}6{x}^{2},\text{\hspace{0.17em}}{(x-y)}^{4}$
$5{x}^{2}+3x-3x{y}^{7}+(x-y)({x}^{3}-6)$
$5{x}^{2},3x,-3x{y}^{7},\text{\hspace{0.17em}}(x-y)({x}^{3}-6)$
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