Are triple brackets on the Foundation paper?

No. Foundation tier A4 asks only for the product of two binomials. Higher tier extends this to two or more, and Edexcel restricts the extension to three linear expressions, so a triple bracket answer is always a cubic.

How many marks are expanding brackets questions worth on Edexcel Higher?

A single bracket is normally 1 mark and a double bracket 2. Expanding and simplifying three brackets is usually 3 marks: one for the first product, one for the complete second expansion, one for the simplified cubic. Expansions also appear inside area, perimeter and proof questions, where they earn the opening method mark.

Does $(x + 3)^2$ equal $x^2 + 9$?

No. (x + 3)^2 means (x + 3)(x + 3), which expands to x^2 + 6x + 9. Put x = 2 into both: the bracket gives 25 while x^2 + 9 gives 13. The middle term 6x comes from the two cross products and never disappears.

Is expanding brackets on the non-calculator paper?

It can be on any of the three papers. The arithmetic involved is small enough that a calculator gives you no advantage, so Paper 1 sets these questions as often as Papers 2 and 3.

Expanding Brackets - Edexcel GCSE Higher Maths

Typically 3-6 marks per paper, plus expansions hidden inside longer questions · Spec 1MA1

Expanding brackets is part of spec point A4 on Edexcel's 1MA1 specification: multiplying a single term over a bracket, and expanding the products of two or more binomials. Foundation tier stops at two binomials. Higher tier takes the wording literally, and Edexcel's teaching guidance limits the extension to products of three linear expressions, so the largest thing you will ever be asked to expand is a cubic such as $(x+1)(x+2)(x+3)$ .

Single and double brackets turn up early on all three papers, either as a short 'expand and simplify' opener or buried inside a longer question about area, perimeter or an algebraic proof. Triple brackets usually stand alone as a 3-mark question. None of it needs a calculator, so Paper 1 carries these questions as readily as Papers 2 and 3; on the calculator papers the arithmetic is still trivial and the bookkeeping is still the hard part.

Edexcel mark schemes for a double bracket give the method mark for three of the four products being right, or all four right ignoring signs, which tells you exactly where the marks leak: signs, and terms that never got written down. The triple bracket version carries two method marks, one for the first product and one for a complete second expansion, before any accuracy mark is available. Write every term out before you collect anything, and read 'expand and simplify' as two separate instructions, because an uncollected $3x + 4x$ throws away the final mark.

Worked example

Expand and simplify

(x + 2)(x - 3)(2x + 1)

[3 marks]

Take any two brackets first. Using the first pair: $(x+2)(x-3) = x^2 - 3x + 2x - 6 = x^2 - x - 6$ .
M1: a correct product of two of the linear expressions (three of the four terms correct is enough for this mark)
Multiply every term of $x^2 - x - 6$ by each term of $(2x + 1)$ : $2x^3 + x^2 - 2x^2 - x - 12x - 6$ .
M1: a complete expansion, all six products present, followed through from their quadratic
Collect like terms: $2x^3 - x^2 - 13x - 6$ .
A1: fully simplified cubic; six uncollected terms score the two method marks only

Practice questions

These are original questions in Edexcel 1MA1 Higher style, covering single brackets, double brackets, squaring a bracket and the Higher-only triple brackets. Nothing here needs a calculator, so work as though you were on Paper 1 and write down every product before collecting like terms. Type algebra the way you would write it, for example $x^2+6x+9$ ; any equivalent form is marked correct.

No account needed: the questions below are always free to check, plus 8 extra questions today. Your score so far updates as you go.

Question 1 Warm-up [1 mark]

Expand $\frac{1}{3}(9x - 6)$ .

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 2 Warm-up [2 marks]

Expand and simplify $(x + 3)^2$ .

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 3 Exam pace [3 marks]

A rectangle has width $(x + 3)$ cm and length $(2x - 1)$ cm. Write an expression for its area in square centimetres, expanded and simplified.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 4 Exam pace [3 marks]

A rectangle has width $(2x - 5)$ cm and length $(3x + 4)$ cm. Write an expression for its perimeter in centimetres, expanded and simplified.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 5 Exam pace [2 marks]

A square has sides of length $(x + 6)$ cm. Write an expression for its area in square centimetres, expanded and simplified.

Your expression (equivalent forms accepted, e.g. 2(x+3) or 2x+6)
Question 6 Exam pace [2 marks]

$(x + 3)(x + n) = x^2 + x - 6$ for all values of $x$ . Find the value of $n$ .

Your answer (fractions like 1/2 are fine)

Common mistakes examiners see

Expanding $-4(2x - 5)$ as $-8x - 20$ , copying the second sign straight out of the bracket.

Multiply the sign as well as the digit: $-4 \times -5 = +20$ , so the answer is $-8x + 20$ . Write the multiplier with its sign attached, as $(-4)$ , and the double negative stops catching you.
Writing $(x + 3)^2$ as $x^2 + 9$ . Substituting $x = 2$ exposes it immediately: the bracket gives 25, the wrong version gives 13.

Rewrite the square as $(x+3)(x+3)$ before multiplying anything. The middle term is the sum of the two cross products, $3x + 3x = 6x$ , so the expansion is $x^2 + 6x + 9$ .
Producing three terms from a double bracket instead of four, usually by losing the inside product, so $(x - 3)(x + 5)$ comes out as $x^2 - 15$ .

Count to four before you simplify. A 2 by 2 grid forces every cell to be filled; three correct products out of four earns the method mark, but only four earns the answer mark.
Subtracting a bracket and changing the sign of the first term only: $7(x + 2) - 3(x - 4)$ written as $7x + 14 - 3x - 12 = 4x + 2$ .

Treat the minus sign as part of the multiplier, so it is $-3$ times $(x - 4)$ , giving $-3x + 12$ and a final answer of $4x + 26$ . Circle the whole $-3$ before you distribute it.
In a triple bracket, multiplying the quadratic by the $x$ term of the last bracket and forgetting the constant, so the cubic arrives with three terms instead of four.

Write the second multiplication as two rows, the quadratic times $2x$ and then the quadratic times $1$ , and check you have six terms before collecting. The second method mark depends on that expansion being complete.

Frequently asked questions

Are triple brackets on the Foundation paper?: No. Foundation tier A4 asks only for the product of two binomials. Higher tier extends this to two or more, and Edexcel restricts the extension to three linear expressions, so a triple bracket answer is always a cubic.
How many marks are expanding brackets questions worth on Edexcel Higher?: A single bracket is normally 1 mark and a double bracket 2. Expanding and simplifying three brackets is usually 3 marks: one for the first product, one for the complete second expansion, one for the simplified cubic. Expansions also appear inside area, perimeter and proof questions, where they earn the opening method mark.
Does $(x + 3)^2$ equal $x^2 + 9$?: No. $(x + 3)^2$ means $(x + 3)(x + 3)$ , which expands to $x^2 + 6x + 9$ . Put $x = 2$ into both: the bracket gives 25 while $x^2 + 9$ gives 13. The middle term $6x$ comes from the two cross products and never disappears.
Is expanding brackets on the non-calculator paper?: It can be on any of the three papers. The arithmetic involved is small enough that a calculator gives you no advantage, so Paper 1 sets these questions as often as Papers 2 and 3.

Expanding Brackets - Edexcel GCSE Higher Maths

Worked example

Practice questions

Common mistakes examiners see

Frequently asked questions

Related topics