4.1 Algebraic expressions

$x+4$ is an expression.

$7y$ is an expression.

$\frac{x-3x^{2}y}{7+9x}$ 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 $8\cdot 1$ .

$3x^4+6x^2+5x+8$ .

This expression has four terms: $3x^4,6x^2,5x,$ and 8.

$15y^8$ .

In this expression there is only one term. The term is $15y^8$ .

$14x^{5}y+{(a+3)}^2$ .

In this expression there are two terms: the terms are $14x^{5}y$ 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.

$p^4-7p^3-2p-11$ .

Associating the sign with the individual quantities we see that the terms of this expression are $p^4,-7p^3,-2p,$ and $-11$ .