Expanding Brackets

Expanding Brackets

Pick single, double or three brackets and practise.

Expand one line at a time

Most marks are lost in the middle of an expansion, not at the start. A term gets missed, a sign flips, or two like terms get collected before every product is written down. This tool splits the job in two so you can see exactly where yours goes wrong: press Expand to write out every product, then press Simplify to collect the like terms.

Work the question out yourself first, on paper or in your head. Then reveal it and mark yourself. Nothing is timed.

Single brackets

Everything inside the bracket gets multiplied by the thing outside it, including the sign.

Expand3(x + 4) = 3 × x + 3 × 4
Answer3x + 12

Double brackets

Every term in the first bracket multiplies every term in the second, so two brackets of two terms give four products. Write all four down before you collect anything.

Expand(x + 2)(x + 5) = x2 + 5x + 2x + 10
Simplifyx2 + 7x + 10

Three brackets

Pick any two brackets and multiply them out first, simplify that, then multiply the result by the bracket you have left. The order you choose does not change the answer, so pick the pair that looks easiest.

First pair(x + 1)(x + 2) = x2 + 3x + 2
Then(x2 + 3x + 2)(x + 3)
Answerx3 + 6x2 + 11x + 6

The three mistakes worth watching for

  • A missed product. Two brackets of two terms give four products every time. Count them before you collect.
  • A dropped minus. The sign in front of a term travels with it. In (x − 3)(x + 4) the −3 multiplies both terms in the second bracket.
  • Collecting too early. Only terms with exactly the same power of x can be added. 5x and 2x collect; x2 and 2x never do.