How to collect like terms in algebra

  • Objects are often represented in algebra by a single letter.

  • Like terms share the same letter(s) and power(s), eg 𝑥 or 𝑥²

  • Algebraic expressions can be collected together if they are like terms. This is done by adding or subtracting.

Find out how to collect like terms in algebra

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How to represent a problem using terms

3 apples and 2 plums can be represented as:

3a + 2p

If we were to add a further 2 apples and 4 plums to this, we would represent this as:

3a + 2a + 2p + 4p

3a, 4p etc. are called terms. Numbers without letters, are also known as terms.

What are 'like' terms?

Terms that contains the same letter(s) or power(s) are called like terms:

e.g. a, -21a and 550a are like terms. 13p, 440p and -2p are like terms. And 𝑥², 70𝑥² and -23𝑥² are all like terms, too.

How to collect terms

Example

3a + 2p + 2a + 4p

Firstly, re-write the equation so that the like terms are together:

3a + 2a + 2p + 4p

Finally use addition to collect them:

5a + 6p

Collecting terms with different mathematical signs

When collecting terms, the sign at the front of the number (co-efficient) tells us if we need to add or subtract them.

Example

3t - 2y + 10t - y - 12

Firstly, re-write the equation so that the like terms are together:

3t + 10t - 2y - y - 12

Finally, add or subtract where appropriate:

13t - 3y - 12

Like terms quiz

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