Simplify Expressions
Simplifying expressions involves combining like terms and expanding brackets to write algebraic expressions in their most compact form. A like term contains the same variable raised to the same power, such as 3x and 7x, which combine to give 10x. This fundamental skill appears throughout Year 6 and Year 7 of the UK National Curriculum, forming the foundation for solving equations and manipulating formulae.
Why it matters
Simplifying expressions underpins virtually every area of advanced mathematics, from solving quadratic equations in GCSE Higher to calculating compound interest in financial mathematics. Engineers use simplified expressions when designing structures—a bridge calculation might start as 15F + 8F - 3F and simplify to 20F to find the total force. In computer programming, simplified expressions run faster and use less memory. Year 7 students encounter this when working with perimeter formulae: a rectangle with sides (3x + 2) and (5x - 1) has perimeter 16x + 2 after simplification. The skill directly supports algebraic manipulation needed for GCSE topics including factorising, solving simultaneous equations, and working with algebraic fractions. Without mastering simplification, students struggle with more complex algebraic processes throughout Key Stage 4.
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: 2x + 3x
Answer: 5x
- Identify like terms → 2x and 3x — Both terms contain the variable x, so they are like terms.
- Add the coefficients → 2 + 3 = 5 — Add the numbers in front of x.
- Write the result → 5x — 2x + 3x = 5x.
Simplify: 3n + 3a + 6n + 1a
Answer: 9n + 4a
- Group like terms → (3n + 6n) + (3a + 1a) — Collect n-terms together and a-terms together.
- Combine like terms → 9n + 4a — 3 + 6 = 9 for n; 3 + 1 = 4 for a.
Expand: 9(5x + 11)
Answer: 45x + 99
- Multiply 9 by the first term → 9 × 5x = 45x — Distribute the factor to the first term inside the brackets.
- Multiply 9 by the second term → 9 × 11 = 99 — Distribute the factor to the second term.
- Write the result → 45x + 99 — 9(5x + 11) = 45x + 99.
Common mistakes
- Combining unlike terms incorrectly, such as writing 3x + 2y = 5xy instead of leaving it as 3x + 2y
- Adding coefficients when multiplying terms, producing 2x × 3x = 5x² instead of the correct 6x²
- Ignoring the invisible coefficient of 1, calculating x + 3x = 3x instead of 4x
- Expanding brackets incorrectly by only multiplying the first term, giving 4(x + 3) = 4x + 3 instead of 4x + 12