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Fully factorise 6x + 9.
3(2x + 9), by only dividing the first term by the common factor 3(2x + 3)
Algebra is a core part of GCSE Maths. Revise the key concepts and common mistakes below, then lock them in with the free games.
Key concepts Expanding Multiplying out the brackets in an expression
Factorising The reverse of expanding — putting brackets back
Single bracket One bracket like 3(x + 4) to multiply out
Double bracket Two brackets multiplied, like (x+2)(x+3)
Common factor A number or letter that divides every term
FOIL First, Outer, Inner, Last — order for double brackets
Linear equation An equation where the highest power of x is 1
Simultaneous equations Two equations solved together for two unknowns
Elimination Adding or subtracting equations to remove a variable
Substitution method Putting one equation into the other to solve
Forming an equation Turning a worded problem into algebra
Balance method Doing the same operation to both sides
Variable A letter standing for an unknown number
Expression Numbers and letters combined, with no equals sign
Show all 14 key concepts What your exam board covers Where Algebra sits in each exam board's specification. Tap a board to see what it lists.
AQA Algebra Spec 8300 Notation, vocabulary and manipulation Graphs Solving equations and inequalities Sequences Source: AQA GCSE Mathematics (8300) specification — Subject content , accessed 23 June 2026.
CCEA Number Spec 2210 Part of: Content domains (across the units)
Source: CCEA GCSE Mathematics (2017) specification , accessed 9 July 2026.
Edexcel Algebra Spec 1MA1 Notation, vocabulary and manipulation Graphs Solving equations and inequalities Sequences Source: Pearson Edexcel GCSE (9–1) Mathematics (1MA1) specification , accessed 23 June 2026.
Eduqas/WJEC Algebra Spec C300QS Notation, vocabulary and manipulation Graphs Solving equations and inequalities Sequences Source: Eduqas GCSE Mathematics specification , accessed 9 July 2026.
OCR Algebra Spec J560 Algebraic expressions Algebraic formulae Algebraic equations Algebraic inequalities Language of functions Sequences Graphs of equations and functions Straight line graphs Transformations of curves and their equations Interpreting graphs Source: OCR GCSE (9–1) Mathematics (J560) specification , accessed 23 June 2026.
Cambridge IGCSE Algebra and graphs Spec 0580 Introduction to algebra Algebraic manipulation Algebraic fractions Indices II Equations Inequalities Sequences Proportion Graphs in practical situations Graphs of functions Sketching curves Differentiation Functions Source: Cambridge IGCSE Mathematics (0580) syllabus , accessed 23 June 2026.
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Common mistakes to avoid Questions where students often pick the tempting wrong answer — make sure you know the right one:
Fully factorise 6x + 9. ✗ 3(2x + 9), by only dividing the first term by the common factor. ✓ 3(2x + 3) — take out the common factor 3.
Expand 3 - (x - 4). ✗ 3 - x - 4 = -1 - x, by only applying the minus to the first term inside. ✓ 7 - x — the minus sign outside the bracket changes the sign of every term inside (3 - x + 4).
When solving 3x = 12, what do you do to both sides? ✗ Subtract 3 from both sides because 3 was multiplying x. ✓ Divide both sides by 3 to get x = 4.
What is the value of x^0 (for x not equal to zero)? ✗ x^0 equals 0 because raising something to the zero gives nothing. ✓ 1 — any non-zero number to the power of zero equals 1.
What does x^(1/2) mean? ✗ x^(1/2) means x divided by 2 — half of x. ✓ The square root of x (the positive root when x is positive).
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