Algebra: Expressions and Equations

Algebra is the language of mathematics. It allows us to generalise, describe patterns, and solve problems using letters to represent unknown or variable quantities.

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Algebraic Notation

Notation	Meaning
ab	a × b (no multiplication sign)
3y	3 × y
a²	a × a
a/b	a ÷ b
(a + b)	a and b treated as a single group

Terms: parts of an expression separated by + or −. In 3x² − 2x + 5, the terms are 3x², −2x, and 5. Coefficient: the number in front of a variable. In 3x², the coefficient is 3. Constant: a number with no variable. In 3x² − 2x + 5, the constant is 5.

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Substitution

Replace each letter with its given value and calculate using BIDMAS.

Example: If a = 3 and b = −2, find 4a² − 3b. = 4(3²) − 3(−2) = 4(9) + 6 = 36 + 6 = 42

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Simplifying Expressions — Collecting Like Terms

Like terms have identical letter parts (including powers).