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`.
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?
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.