Expanding Brackets Question Generator
Two brackets to multiply out. The interesting part of this skill is not the multiplication, it is remembering that four products come out and two of them combine — which is exactly where negatives cause trouble. The working here writes all four separately before collecting, so a wrong middle term is easy to trace back to the cross product that caused it.
What this generator does
Generates a product (ax + b)(cx + d) and asks for it multiplied out. The answer is the three coefficients of the expansion, and the working names each partial product — the x² term, the two cross terms, and the constant — before collecting.
How to use this tool
- Choose how many products you want and how big the numbers get.
- Multiply out and simplify each one.
- Reveal the answers to check the three coefficients.
- Show the working to see the cross terms written out before they are collected.
Understanding the controls
- How many questions
- Between 1 and 20. These are quick, so a set of fifteen is still only a few minutes of work.
- Level
- Gentle fixes both x coefficients at one, which is the form most people meet first. Standard and stretch allow coefficients on both, which is where the cross terms stop being obvious.
- Seed
- The same word gives the same products, so a set can be reissued exactly.
- Show the answers / working
- The simplified expansion, or every partial product on the way to it.
Common use cases
- Drilling double brackets before moving on to factorising
- Practising the sign of the middle term where one bracket is negative
- A starter that takes two minutes and needs no context
- Building up to expansions where both x coefficients are greater than one
- Setting the same five questions to a group from one seed
How this generator works
Four integers are drawn for the two brackets, and the expansion is computed as ac, ad + bc and bd. The check multiplies the stated factors back out and compares all three coefficients, so an expansion that does not correspond to its own brackets cannot be shown.
Randomness and fairness
The bracket coefficients are drawn at random; the expansion is arithmetic and is not. Seeded sets are reproducible and therefore explicitly not cryptographically secure, and unseeded ones use the browser's cryptographically secure generator.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Both brackets are linear. Products of three brackets, and squares written as (ax + b)², are not generated.
- Coefficients are whole numbers, so fractional and surd expansions are out of scope.
- No expansion here needs a common factor taken out first.
- The tool does not check your answer — it reveals its own for you to compare.
- Question sets are not stored, so seed one you want to keep.
Privacy and your data
Products are generated locally in your browser. No question, seed or setting leaves the page or survives it.
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