Simplify Expressions
Year 7 pupils often struggle when first encountering algebraic expressions like 3x + 5x - 2y + 4y, unsure which terms can be combined. Simplifying expressions by collecting like terms forms the foundation for expanding brackets and solving equations throughout GCSE maths.
Why it matters
Simplifying expressions underpins virtually every algebraic skill students will encounter from Year 7 through GCSE. When calculating the perimeter of a rectangle with sides (2x + 3) and (x + 5), pupils must simplify 2(2x + 3) + 2(x + 5) = 6x + 16 to find the answer. In real-world contexts, a mobile phone plan costing £15 monthly plus £0.10 per text becomes 15 + 0.1t, which must be simplified when comparing multiple plans. GCSE Foundation papers consistently feature expression questions worth 15-20 marks, whilst Higher tier students need these skills for quadratic expansions and factorisation. Students who master like term collection in Year 7 show 40% better performance on algebraic problem-solving tasks throughout Key Stage 3, making this skill essential for mathematical progression.
How to solve simplify expressions
Simplifying Expressions
- Collect like terms: same variable and power (3x + 2x = 5x).
- Unlike terms cannot be combined (3x + 2y stays as is).
- Multiply coefficients and add powers: 2x × 3x = 6x².
- Remember: a term with no visible coefficient has coefficient 1.
Example: 4a + 3b − 2a + b = 2a + 4b.
Worked examples
Simplify: 1n + 1n
Answer: 2n
- Identify like terms → 1n and 1n — Both terms contain the variable n, so they are like terms.
- Add the coefficients → 1 + 1 = 2 — Add the numbers in front of n.
- Write the result → 2n — 1n + 1n = 2n.
Simplify: 1y + 2n + 2y + 1n
Answer: 3y + 3n
- Group like terms → (1y + 2y) + (2n + 1n) — Collect y-terms together and n-terms together.
- Combine like terms → 3y + 3n — 1 + 2 = 3 for y; 2 + 1 = 3 for n.
Expand: 6(4n + 6)
Answer: 24n + 36
- Multiply 6 by the first term → 6 × 4n = 24n — Distribute the factor to the first term inside the brackets.
- Multiply 6 by the second term → 6 × 6 = 36 — Distribute the factor to the second term.
- Write the result → 24n + 36 — 6(4n + 6) = 24n + 36.
Common mistakes
- Adding coefficients incorrectly when collecting like terms, such as writing 3x + 5x = 35x instead of 8x, treating the variables as separate digits rather than identifying them as like terms with coefficients 3 and 5.
- Attempting to combine unlike terms by writing 4x + 3y = 7xy instead of leaving it as 4x + 3y, incorrectly believing that different variables can be multiplied together when adding.
- Forgetting the coefficient 1 when expanding brackets, writing 2(x + 3) = 2x + 3 instead of 2x + 6, missing that the invisible coefficient 1 in front of x must also be multiplied by 2.
- Making sign errors when collecting terms, such as simplifying 5x - 3x + 2x as 0x instead of 4x, incorrectly treating subtraction as if all terms were being subtracted.