Expanding and factorising

Expanding removes brackets by multiplying everything inside by what is outside. Factorising is the reverse: take out the highest common factor and put brackets back.

Key facts

  • a(b + c) = ab + ac
  • Two brackets: multiply every term by every term (FOIL or a grid).
  • To factorise, find the HCF of all the terms, then divide each term by it.
  • Check by expanding your answer.

Worked examples

Example 1

Expand 3(2x − 5).

  1. 3 times 2x. 3 × 2x = 6x
  2. 3 times −5. 3 × (−5) = −15
  3. So 6x − 15

Answer: 6x − 15

Example 2

Expand and simplify (x + 4)(x + 3).

  1. First, Outside, Inside, Last. x² + 3x + 4x + 12
  2. Collect like terms. x² + 7x + 12

Answer: x² + 7x + 12

Example 3

Factorise 12x + 18.

  1. The HCF of 12 and 18 is 6. 12x ÷ 6 = 2x, 18 ÷ 6 = 3
  2. Put the 6 outside. 6(2x + 3)
  3. Check by expanding. 6 × 2x + 6 × 3 = 12x + 18

Answer: 6(2x + 3)