Grade 10 · Theory
Products and factorisation
Algebraic expressions · about 3 min
Visual overview: Products and factorisation1 MIN READ
2 study sections · pause after each one and recall the key ideaExpanding multiplies brackets out; factorising puts them back. Recognising standard forms saves you enormous time.
Key points- 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.
EXAM TIP
check every factorisation by expanding it back mentally — it costs seconds and catches sign errors.