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Pearson Edexcel 4MA1 IGCSE  ·  Topic G2.7

G2.7 Writing Algebraic Expressions

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01 — Explanation

What's the difference between an expression and an equation?

An expression is a mathematical phrase with no equals sign, such as 2n−32n - 3 for "3 less than double a number". It has a value depending on nn, but there's nothing to solve. An equation contains an equals sign and asserts two expressions are equal, such as 8y−66=2y8y - 66 = 2y, which can be solved for yy.

Golden Rule

if there's no equals sign, don't try to solve it. The most common error at this level is forming a correct expression like 2n−32n-3 and then setting it equal to zero out of habit.

02 — Explanation

How do I translate words into algebra?

Learn the keyword-to-operation links: "more than / sum / total" → add; "less than / difference" → subtract; "times / product / lots of" → multiply (write the number before the letter, e.g. 3n3n not n3n3, to avoid confusion with n3n^3); "shared between / divided by" → divide.

Common Mistake

"less than" reverses the natural word order. "hh less than gg" means start with gg and take away hh, giving g−hg-h — not h−gh-g.

03 — Explanation

How do I combine several operations, and when do I need brackets?

Work through the sentence in the order the operations are described, but add brackets whenever a single operation must apply to an entire previous result.

  • "tt add 2, then multiplied by 5" → the addition must happen first and the whole result gets multiplied: 5(t+2)5(t+2).
  • Without brackets, 5t+25t+2 would mean "multiply by 5, then add 2" — a different instruction entirely.

04 — Explanation

How do I form an expression from a worded problem with several quantities?

Identify the unknown, express every other quantity in terms of it, then combine and simplify as instructed.

Example: a rectangle has length 3x+23x+2 and width x−1x-1. Find its perimeter in simplest form.

P=(3x+2)+(x−1)+(3x+2)+(x−1)P = (3x+2)+(x-1)+(3x+2)+(x-1)

Grouping the xx-terms (3x+x+3x+x=8x3x+x+3x+x=8x) and the numbers (2−1+2−1=22-1+2-1=2):

P=8x+2P = 8x + 2

05 — Worked example

Worked exam-style question

A child's cinema ticket costs £x\pounds x. An adult's ticket costs £5\pounds 5 more than a child's.

(a) Write an expression for the price of an adult's ticket.

(b) Write an expression, in its simplest form, for the cost of one adult's ticket and two child's tickets.

(a) "£5 more than xx" translates directly: x+5x+5.

(b) One adult plus two children: (x+5)+2x(x+5) + 2x. Collecting like terms: 3x+53x + 5.

Exam Tip

write the unsimplified expression first — (x+5)+2x(x+5)+2x — before collecting terms. This secures the method mark even if a slip occurs during simplification, and it also protects you from the most serious error on this topic: accidentally trying to "solve" the finished expression because it looks like an equation.

06 — Explanation

How do I avoid answering a different question from the one asked?

Before finalising an answer, re-read the question's exact final phrase. Examiner reports for this topic repeatedly note that students correctly translate most of a scenario but then answer, say, "the total number of boxes" when the question asked for "the total number of items inside the boxes". Underlining the command phrase on first reading — and checking your final expression against it — catches this reliably.