Expanding brackets means multiplying expressions correctly to remove brackets. It is closely linked to simplifying expressions and factorising, and is an essential step in algebraic manipulation.
Expanding brackets means multiplying the term outside the bracket by every term inside the bracket.
This is a key GCSE algebra skill because it appears in simplifying expressions, factorising, solving equations and working with quadratics.
A group of terms written together, such as \(x + 5\).
Multiply out the bracket so the expression no longer stays in bracket form.
One part of an expression, separated by + or − signs.
The number multiplying the variable, such as 4 in \(4x\).
A mathematical phrase with numbers, letters and operations.
Collect like terms and write the final answer in its shortest correct form.
\(2(x+5)=2x+10\)
\(3(x-4)=3x-12\)
\(-2(x+3)=-2x-6\)
\(2(x+4)+x=3x+8\)
\(5(a+2)\)
\(4(y-7)\)
\(-3(2x+1)\)
\(2(x+3)+4x\)
Expanding brackets means multiplying everything inside the bracket by the term outside. This is based on the distributive property.
After expanding, you often need to combine like terms.
When expanding two brackets, each term in the first bracket multiplies each term in the second bracket.
Exam-style questions inspired by Edexcel GCSE Mathematics.
Expand \( 3(x + 4) \).
Expand \( 5(a - 2) \).
Expand \( -2(y + 6) \).
Expand \( 4(2x - 3) \).
Expand and simplify \( 6(3p + 2) \).
Exam-style questions based on the AQA GCSE Mathematics specification, focusing on accuracy and algebraic fluency.
Expand \( x(x + 5) \).
Expand \( (x + 3)(x + 4) \).
Expand \( (x + 7)(x - 2) \).
Expand and simplify \( (2x + 3)(x + 5) \).
A student expands \( (x + 4)^2 \) as \( x^2 + 16 \). Explain the mistake and give the correct answer.
Exam-style questions aligned with OCR GCSE Mathematics, emphasising reasoning, negative signs, and special products.
Expand \( (x + 5)^2 \).
Expand \( (x - 6)^2 \).
Expand \( (x + 3)(x - 3) \).
Expand and simplify \( (3x - 2)(2x + 5) \).
Expand \( -3(x - 4) \).
Check how many terms are inside the bracket.
Multiply the outside term by every inside term.
Keep positive and negative signs correct.
Simplify the final expression if needed.
Only multiplying one term inside the bracket instead of all of them.
Forgetting that a negative outside affects every term inside.
Leaving the answer unsimplified when like terms can still be collected.
Skipping one of the four products.
These are common mistakes students make when expanding brackets in GCSE Maths.
A student multiplies only the first term inside the bracket.
Every term inside the bracket must be multiplied. For example, \(3(x + 4) = 3x + 12\), not \(3x + 4\).
A student does not apply the negative to all terms.
A negative sign in front of brackets changes the sign of every term. For example, \(-(x + 5) = -x - 5\).
A student gets positive and negative results mixed up.
Check signs carefully: positive × positive = positive, negative × positive = negative, and negative × negative = positive.
A student expands correctly but leaves like terms uncombined.
After expanding, always collect like terms to fully simplify the expression.
A student forgets to multiply one pair of terms in expressions like \((x + 2)(x + 3)\).
In double brackets, every term in the first bracket must multiply every term in the second bracket. Use a systematic method such as FOIL or a grid.
Practise expanding single and double algebraic brackets.
Start with single brackets and basic expansion.
Expand: \(3(x + 4)\)
Expand: \(5(x + 2)\)
Expand: \(4(x - 3)\)
Expand: \(7(y + 5)\)
Expand: \(2(3x + 4)\)
Expand: \(3(2a - 1)\)
A student says \(3(x + 4) = 3x + 4\). What mistake did they make?
Expand: \(6(2x + 3)\)
Which is equal to \(5(x + 6)\)?
Expand: \(9(x - 2)\)
Expand double brackets and handle algebraic multiplication.
Expand: \((x + 3)(x + 2)\)
Expand: \((x + 4)(x + 1)\)
Expand: \((x + 5)(x - 2)\)
Expand: \((x - 3)(x + 6)\)
Expand: \((2x + 3)(x + 4)\)
Expand: \((3x + 2)(x + 5)\)
A student expands \((x + 2)(x + 3)\) to \(x^2 + 6\). What did they miss?
Expand: \((x - 4)(x - 3)\)
Which expression expands to \(x^2 + 9x + 20\)?
Expand: \((2x - 3)(x + 7)\)
Expand: \((x + 3)^2\)
Expand: \((x + 5)^2\)
Expand: \((x - 4)^2\)
A student says \((x + 3)^2 = x^2 + 9\). What mistake did they make?
Expand: \((x + 2)(x - 2)\)
Expand: \((2x + 3)^2\)
Practise this topic with interactive games.
Multiplying out brackets.
Multiply each term in the first bracket by each term in the second.
Forgetting to multiply all terms.