 What you need to know

Things to remember:

• We look at terms individually.
• We include the operator (+ or -) before the numbers and variables as part of the term.
• If there isn’t an operator before a term, then it is a +.

There are five different types of terms:

Numbers by themselves

4          -8         1          -1         0.5       0.25     $\frac{3}{5}$           $\frac{12}{13}$

Variables by themselves

$a$             $g$             $h$             $z$

Variables multiply by numbers

$2a$           $5g$           $0.4h$         $\frac{3}{5}z$

Variables multiplied together

$ab$            $gh$            $ch$            $bz$

Variables and numbers multiplied together

$2ab$          $fgh$          $0.4ch$       $\frac{3}{5}bz$

How many terms are there in the following expression?

$$3x+3-4+y-24+3xy$$

If we read it going from left to right we can see: 3, x, 3, 4, y, 24, 3, x, and y. So there are 9 terms… But not quite, because the last 3, x, and y are actually together to make 1 term. So, the best way is to split it up the terms by the operators (+ and -)

$$(3x)(+3)(-4)(+y)(-24)(+3xy)$$

Now that we have split them up, we can just count up the brackets; there are 6 terms.

How many terms are there in the following expression?

$$9z^2-5x-13y+6y$$

$$(9z^2)(-5x)(-13y)(+6y)$$

There are 4 terms in the expression

How many terms are there in the following expression?

$$a^3b^2-5xyz+2-2$$

Hint: Although the $2-2=0$, we have to count the terms separately first.

$$(a^3b^2)(-5xyz)(+2)(-2)$$

There are 4 terms in the expression

Example Questions

$$y-7z^2+3y+2x-4+3x+2$$

$$(y)(-7z^2)(+3y)(+2x)(-4)(+3x)(+2)$$

There are 7 terms in the expression

$$-a+a^2-a^3+ab-ab^2+ab^3$$

$$(-a)(+a^2)(-a^3)(+ab)(-ab^2)(+ab^3)$$

There are 6 terms in the expression