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OCR asks you to "manipulate polynomials algebraically", and expanding is the direction of travel that turns a product into a sum. It looks like GCSE revision until the brackets multiply up to three at a time and the powers start interacting — at which point a system beats guesswork.
The big picture
Expanding is rarely the point of an A-Level question; it is the step you do on the way to the point. You expand to differentiate a product without the product rule, to find where two curves meet, to check a factorisation, to get a binomial expansion into a usable form. Because it is never the goal, it is also where marks quietly leak: a sign lost in the third term of an expansion propagates through the entire rest of the question and there is no natural moment to catch it. The habit worth building here is not speed but a check you can trust.
What you'll be able to do
Multiplying a bracket by a term outside means multiplying term inside, carrying its sign with it. .
The place this goes wrong is a minus sign outside. In , both terms change: and , giving . The second sign flipping is the step people skip.
Tip — Treat a minus outside the bracket as the whole bracket. Written that way there is no separate rule to remember and no sign to forget.
Multiplying means every term in the first bracket meets every term in the second: . Two terms times two terms gives four products, always, before any collecting.
That is the check. A 2-by-2 expansion that yields three terms before simplification has lost one. A 2-by-3 expansion should produce six. Counting products is faster than re-doing the expansion and it catches the omission rather than the arithmetic.
Collect by power rather than by position. Writing the s, then the s, then the s, then the constants keeps a long expansion ordered and makes a missing term visible as a gap.
Three expansions recur so often they are worth knowing by sight rather than deriving each time. The two squares differ only in the sign of the middle term; the third loses its middle term entirely because the cross products cancel.
The difference of two squares is the one that earns its keep beyond expanding — it is what makes conjugates work when rationalising surds, and it is the fastest factorisation to spot in reverse.
Tip — is never . The middle term is the whole content of the identity — dropping it is the most-repeated error in algebra.
For three brackets, multiply two of them out completely, tidy the result, then multiply that by the third. Trying to track all products at once invites omissions.
Choose the easy pair first. If two of the brackets are and , start there — the difference of two squares collapses them to and halves the work.
The constant term of the final answer is always the product of the three constants — here . Checking that one number takes a second and catches a surprising share of errors.
Think like an examiner
Common misconceptions
Expansion identities
Stretch yourself
Find the coefficient of in the expansion of , without expanding the whole product.
Hint — An term is made by taking from two brackets and the constant from the third. List the three ways.
Questions students ask
Key takeaways
How this fits the course
Test yourself
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Real past-paper questions on Expanding Brackets, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.