Algebraic notation and simplification

CCEA expects fluent use of algebraic conventions on every paper. Marks are awarded for correctly written answers — not just correct values.

Conventions you must use

• Multiplication is written by juxtaposition: write 3a, not 3 × a or 3·a.
• Division is written as a fraction: a/2, not a ÷ 2.
• Powers: a × a = a², a × a × a = a³. Write the index small and to the upper right.
• Coefficients come first: 5x, not x5. Letters in alphabetical order: 3abc, not 3cba.

Like terms

Terms are like when they have the same letters with the same powers. Combine them by adding/subtracting coefficients.

Example: 4x + 7y − x + 3y = (4 − 1)x + (7 + 3)y = 3x + 10y.

Be careful with signs — the sign in front belongs to the term that follows it.

Multiplying terms

Multiply numbers, then add indices on matching letters.

Example: 4x²y × 3xy³ = 12x³y⁴.

Dividing terms

Divide numbers, then subtract indices.

Example: 12a⁵b³ ÷ 4a²b = 3a³b².

Substitution

Replace each letter with its given value. Always use brackets when substituting negatives.

Example: if x = −2, find 3x² − 5x + 1. 3(−2)² − 5(−2) + 1 = 3(4) + 10 + 1 = 23.

Common CCEA exam tip

When asked to simplify — collect like terms only. When asked to expand and simplify — multiply out brackets first, then collect like terms. Reading the verb decides which marks are available.