Terms

## Terms

Terms are the different parts of an expression. A term can be a simple number, a letter, or a combination of a number and letters. For example, 25, 6g, 7h and 17bc are all terms.

A taxi company charges for fares at a rate of £2.50 plus £1.05 per kilometre. This can be written as an expression:

Fare in £ = 2.50 + 1.05k, where k is the number of kilometres driven

The 2.50 and 1.05 numbers cannot be added together, because the value of 1.05k changes depending on how many kilometres (k) are driven. The £2.50 and the 1.05k are different terms.

In an expression 3 + 2x + 7x^2 + 4y, the 3, 2x, 7x^2 and 4y are all separate terms. If the letters are different, or have different powers, they are different terms: x, x^2 and x^3 are all different terms.

Terms that can be added together are called like terms. Terms that cannot be added together are called unlike terms.

The number 1 is not normally written at the front of a term: so 1x is written as x.

## Example 1

How many terms are there in this expression: 3 + 2a + 8b + 4c?

There are four terms: the 3 is a term (as it is a number), and each combination of number-letter is also a term.

Is 2n + 4 an expression or a term?