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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,7hand17bc 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 £, 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.

Answer: 4

Example 2

Is 2n + 4 an expression or a term?

When giving an answer to a question like this, also give an explanation.

Answer: It is an expression, as it consists of more than one term.