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Expressions, substitution and formulae
Algebra uses letters to stand for numbers. Learn the vocabulary and how to substitute, and the rest of algebra gets easier.
Key words
An expression has no equals sign: 3x + 2.
An equation can be solved: 3x + 2 = 11.
A formula links quantities: A = lw.
An identity is true for every value: 2(x + 1) ≡ 2x + 2.
An equation can be solved: 3x + 2 = 11.
A formula links quantities: A = lw.
An identity is true for every value: 2(x + 1) ≡ 2x + 2.
Collecting like terms
Only terms with exactly the same letters and powers can be combined.
5a + 3b − 2a + b = 3a + 4b
x2 and x are not like terms.
5a + 3b − 2a + b = 3a + 4b
x2 and x are not like terms.
Substitution
Replace each letter with its value and follow BIDMAS.
If a = 3 and b = −2: a2 − 4b = 9 − (−8) = 17
Put negative numbers in brackets so you do not lose the sign.
If a = 3 and b = −2: a2 − 4b = 9 − (−8) = 17
Put negative numbers in brackets so you do not lose the sign.
Find the value of 3p2 − q when p = −2 and q = 5.
- p2 = (−2)2 = 4
- 3 × 4 = 12
- 12 − 5 = 7
Answer: 7
Expressions have no equals sign, equations can be solved, formulae link quantities, identities are always true. Only like terms combine. Substitute with brackets around negatives.
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