Multiplying Terms
3x means "3 multiplied by x". The multiplying sign is not shown.
If two terms are being multiplied, the number comes first and the variables are usually placed in alphabetical order.
Examples
3q × 4p = 12pq
5a × 6b × 2 = 60ab
Note that in these two examples, the numbers are first and letters (variables) are placed in alphabetical order.
If the variables are the same then exponents are used. (See Topic 37)
Remember 3x.4y means 3x multiplied by 4y (which equals 12xy).
Adding and Subtracting Terms
An expression involving addition and subtraction can be simplified only if it contains liketerms.
Like terms have the same variables (letters) and exponents (indices)
Examples
{ 2a, 4a, -6a } are like terms. a is common to all.
{ x, 3a2, 6 } are unlike terms. There is no common term.
The like terms are collected together and then added or subtracted.
| Examples |
Like or unlike terms?
|
Answers |
|
Simplify:
|
|
4a + 6a
|
like terms
|
4a + 6a = 10a
|
| 12x − 3x |
like terms
|
12x − 3x = 9x |
|
12pq + 4pq
|
like terms
|
12pq + 4pq = 16pq
|
| 12x2 + 10x2 |
like terms
|
12x2 + 10x2 = 22x2 |
| 3p + 4q |
unlike terms
|
3p + 4q cannot be simplified. |
| 4b + 5b2 |
unlike terms
|
4b + 5b2 cannot be simplified. |
|
3c + 4d + 5c
|
some like terms
|
3c + 4d + 5c
= 3c + 5c + 4d
= 8c + 4d
(cannot be simplified further)
|
The Order of Variables and Terms
In a term the variables are usually placed in alphabetical order although the terms are still equal if the variables are not in alphabetical order.
e.g. ab = ba
6pq2 = 6q2p
In an expression the terms can also be arranged in a different order so long as the operation sign moves too.
e.g. a + b = b + a
p − 2q = -2q + p
Dividing Terms
Dividing terms is covered in the extension topic, More Difficult Algebra, Topic 50
|
