Expanding multiplies brackets out; factorising puts them back. Recognising standard forms saves you enormous time.

• Common factor first, always: 6x² + 9x = 3x(2x + 3).
• Difference of two squares: a² − b² = (a − b)(a + b).
• Trinomials: x² + 5x + 6 = (x + 2)(x + 3) — find factors of the constant that add to the middle term.
• Grouping works when there are four terms: ax + ay + bx + by = (a + b)(x + y).

• Factorise — write an expression as a product of its factors.
• Trinomial — an expression with three terms.