GRADE 8 Mathematics ALGEBRA – Algebraic Expressions Notes
MATHEMATICS — ALGEBRA
Subtopic: Algebraic Expressions (age ~13)
An algebraic expression is a combination of numbers, letters (called pronumerals), and operation signs ( +, −, ×, ÷ ). Pronumerals represent unknown or varying numbers. In Kenyan schools you may also hear "letters" or "symbols" used.
- Term: a single number or pronumeral, or product of them (e.g. 5, x, 3y).
- Coefficient: the number multiplied by the pronumeral (in 4x, coefficient is 4).
- Constant: a term with no pronumeral (e.g. 7).
- Like terms: terms with the same pronumeral part (e.g. 2x and −5x are like terms).
Examples
Simple expressions:
- 3x + 5
- 2a − 7
- 4m + 3n − 12
- 5 (no pronumeral) is a constant
Writing expressions from words
Translate by choosing a pronumeral for the unknown and applying operations:
- "The number x increased by 7" → x + 7
- "Three times a number n" → 3n
- "5 less than y" → y − 5 (note order matters)
Evaluating an expression
To evaluate, substitute a number for the pronumeral and follow BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).
Simplifying by collecting like terms
Combine terms that have the same pronumeral.
(5x − 2x) + (3 + 7) = 3x + 10.
Multiplying into brackets (distributive law)
a(b + c) = ab + ac. Use this to expand simple brackets.
Factorising (common factor)
Write terms as a product of a common factor and a bracket.
Using negatives and subtraction
Remember that subtracting a term is same as adding its negative: a − b = a + (−b).
Simple visual: grouping like terms
Practice (try these)
- Write in algebraic form: "Seven more than a number p".
- Evaluate 2a − 3 when a = 4.
- Simplify: 7x − 2x + 6 − 4.
- Expand: 3(2x + 5).
- Factorise: 8y + 12.
- Which are like terms: 4m, m, 4n, −2m?
Answers
- p + 7
- 2×4 − 3 = 8 − 3 = 5
- (7x − 2x) + (6 − 4) = 5x + 2
- 3×2x + 3×5 = 6x + 15
- 4(2y + 3) so common factor 4: 4(2y + 3) (or 4(2y + 3) = 8y + 12)
- Like terms: 4m, m and −2m (they have the pronumeral m); 4n is not like them
Tips: practise writing statements in algebraic form and always check you combine only like terms. Use BODMAS when evaluating.