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

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