Unit 5 sec 2.2 what is a term

Unit 5 sec 2.2 what is a term

16 December 2015

22:10

Some expressions are lists of things that are all added or subtracted. Here is an example

-2xy +3z -y².

The things that are added or subtracted in an expression of this sort are cold the terms. The terms of the expressions above are

-2xy, +3z and -y².

The plus or minus sign at the start of each term is part of the term. Well, you are getting used to working with terms.

You need it to make sure that the sign at the start of each term is included along with the rest of the term.

If the 1^st term of an expression has no sign, then the term is added to the other terms, so really it has a plus sign - it is just that we normally do not write a plus sign in front of the 1^st term of an expression. For example, if you have the expression

4a +c - 7√b – 5,

then you could write a + at the start and mark the terms. When we discussed the terms of expression, we often omit the plus signs. This is convenient in the same way that it is convenient to write the number +3 as 3. So, for example, we might say that the expression

-2xy +3z - y²

has terms

-2xy, 3z and -y².

We never omit the minus sign! And, of course, we never omit the plus sign of a term when writing the term as part of an expression, unless it is the 1^st term.

There is a useful way to think of the relationship between expressions terms.

An expression is equivalent to the sum of its term

the expression on the run is obtained by adding the term of expression (2) on the left. The 2 expressions are equivalent because subtracting y² is the same as adding naked of y².

 Because the order in which numbers are added as a matter, you can change the order of the terms in an expression however you like, and you will obtain an equivalent expression, as long as you keep each term together with its sign. For example, you can swap the order of the 1^st 2 terms in the expression

-2xy+ 3z - y²

to give

3z – 2xy - y²

are you can reverse the original order of the terms to give

-y² + 3z – 2xy.

All 3 of these expressions are equivalent to each other.

Changing the order of the terms simplify an expression, but some methods for simplifying expressions are easier to apply if you arrange the terms 1^st.

The term in an expression may be just a number, like 4, ½ or -5. If so, we say that it is a constant term, I just a constant for short. For example, the expression

3pq -2 + 5p²

has one constant term, -2.

On the other hand, if a term is of the form

a number × a combination of letters,

then the number is called the coefficient of the term, and we say that the term is a term in whatever the combination of letters is. For example

2xy is coefficient 2 and is a term in xy

-3z has coefficient -3 and is a term in z

2/3c² has coefficient 2/3 and is a term in c².

You may be tempted to think that term is like a and -a do not have coefficient. However, because they are equivalent to 1a and -1a, respectively, they have coefficients 1 and -1, respectively.