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.
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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.