11.1 Algebraic expressions

${\displaystyle x+4}$ . In this expression, x and 4 are connected by a "+" sign. Therefore, they are terms. This expression consists of two terms.

${\displaystyle y-8}$ . The expression ${\displaystyle y-8}$ can be expressed as ${\displaystyle y+(-8)}$ . We can now see that this expres­sion consists of the two terms ${\displaystyle y}$ and ${\displaystyle -8}$ .

Rather than rewriting the expression when a subtraction occurs, we can identify terms more quickly by associating the + or - sign with the individual quantity.

${\displaystyle a+7-b-m}$ . Associating the sign with the individual quantities, we see that this expression consists of the four terms ${\displaystyle a}$ , 7, ${\displaystyle -b}$ , ${\displaystyle -m}$ .

${\displaystyle 5m-8n}$ . This expression consists of the two terms, ${\displaystyle 5m}$ and ${\displaystyle -8n}$ . Notice that the term ${\displaystyle 5m}$ is composed of the two factors 5 and ${\displaystyle m}$ . The term ${\displaystyle -8n}$ is composed of the two factors ${\displaystyle -8}$ and ${\displaystyle n}$ .

${\displaystyle 3x}$ . This expression consists of one term. Notice that ${\displaystyle 3x}$ can be expressed as ${\displaystyle 3x+0}$ or ${\displaystyle 3x\cdot 1}$ (indicating the connecting signs of arithmetic). Note that no operation sign is necessary for multiplication.