Expanding and factorising

Every term in one bracket must multiply every term in the other. Keep signs attached to coefficients. Write down all the products before collecting powers. This makes negative signs easier to check.

Before looking for a special pattern, extract any common factor. Multiply your brackets back out to check a factorisation. The identity a² − b² = (a − b)(a + b) is particularly useful for repeated expressions.

Worked example

Factorise 6x² − 5x − 6.

1. The product 6 × (−6) is −36; 4 and −9 add to −5.
2. Write 6x² + 4x − 9x − 6.
3. Group as 2x(3x + 2) − 3(3x + 2).

Answer: (2x − 3)(3x + 2)