Algebraic Expressions
Summary: Algebra uses letters to represent unknown values, forming expressions that can be simplified, substituted into, and expanded using brackets. Tags: concepts math y7 algebra expressions Created: 2026-05-30 Last Updated: 2026-05-30
Content
Algebra concerns representing missing information using letters, known as variables. A constant is a fixed value that does not change. A term is a single number, variable, or product of numbers and variables (e.g. 5x, 3, −2y).
Algebraic Notation
When writing algebra, we follow conventions:
- Omit the multiplication sign: write 3 × m as 3m, not 3 × m
- Write the number before the variable: 4x not x4
- Write variables in alphabetical order: 3ab not 3ba
- Use index notation for repeated variables: x × x = x²
Collecting Like Terms
Like terms have exactly the same variable part. To simplify an expression, add or subtract the coefficients of like terms.
Substitution
Substitution means replacing variables with given numerical values and calculating the result. Always follow the order of operations (BIDMAS).
When substituting into expressions with powers, evaluate the power first: if x = 4, then x² + 3x = 16 + 12 = 28.
Forming Expressions
Translate word problems into algebra by identifying the variable and the operations applied to it.
For geometry problems, use known formulas. A rectangle with length (x + 3) cm and width 5 cm has perimeter 2(x + 3 + 5) = 2x + 16 cm.
Expanding Brackets
To expand a bracket, multiply each term inside the bracket by the term outside.
When expanding with a negative multiplier, be careful with signs: −2(x − 3) = −2x + 6.
Expanding and Simplifying
When two sets of brackets are added, expand each separately then collect like terms.
Index Laws with Algebra
The basic index laws for Year 7:
- Multiplication: aᵐ × aⁿ = aᵐ⁺ⁿ (e.g. x² × x³ = x⁵)
- Division: aᵐ ÷ aⁿ = aᵐ⁻ⁿ (e.g. x⁵ ÷ x² = x³)