The vocabulary of algebra — variables, constants, terms, coefficients and exponents — how to spot like terms, and how to add and subtract them correctly, with worked examples and a quiz.
Algebra is arithmetic with letters standing in for numbers. Before you can simplify or solve anything, you need the vocabulary — because exam questions are written in exactly this language.
1The parts of an expression
Look at the expression 3x² + 5x − 7:
- Terms are the parts separated by + or − signs. Here there are three terms: 3x², 5x and −7.
- Variables are the letters (x) — they stand for numbers that can change.
- Constants are plain numbers with no letter (−7).
- The coefficient is the number in front of a variable — the coefficient of x² is 3, and of x is 5.
- The exponent shows the power of the variable — in 3x² the exponent is 2.
A term keeps the sign in front of it. In 3x² − 7x the second term is −7x, not 7x. Losing that minus sign is one of the biggest causes of lost marks in algebra.
2Like terms
- 13x and 5x — both are x to the power 1 → LIKE terms.Same letter, same power.
- 22x2 is not like 3x.x2 and x are different powers.
- 37y is not like any of the x terms.Different letter altogether.
3Adding and subtracting like terms
You may only add or subtract like terms. Think of it as counting objects: 3 apples + 5 apples = 8 apples, but 3 apples + 5 bananas cannot be combined into one term.
- 1Group the like terms: (7x − 2x) + (3y + 5y).Keep each term's sign with it.
- 27x − 2x = 5x and 3y + 5y = 8y.Add/subtract only the coefficients; the letter stays the same.
- 3Answer: 5x + 8y.Unlike terms simply stay side by side.
- 1Like terms: 4a2 and −a2.Both are a to the power 2.
- 24a2 − a2 = 3a2.a2 means 1a2, so 4 − 1 = 3.
- 3Answer: 3a2 + 3a + 6.3a and 6 have nothing to pair with.
Never do this: 3x + 4 = 7x. The 4 is a constant and 3x has a variable — they are unlike terms and cannot be added.
Practice exercises
Work each one out, then click to reveal the answer.
- 1How many terms are in 5x2 − 3x + 8?
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Three: 5x2, −3x and 8 - 2What is the coefficient of x in 9x − 4?
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9 - 3Name the constant in 2y + 7.
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7 - 4Simplify: 6a + 2a
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8a - 5Simplify: 9m − 4m + 2m
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7m - 6Simplify: 5x + 3y + 2x − y
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7x + 2y - 7Simplify: 4p2 + 3p − 2p2 + p
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2p2 + 4p - 8Simplify: 8 + 3k − 5 + k
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4k + 3
Quick Quiz
4 quick questions on what you just read. Take it when you feel ready.
Now practise it
Download Grade 8 past papers and worksheets on this topic.