MathsGradeUp logoMathsGradeUp
MathematicsGCSE & IGCSE

What is factorising?

Factorising rewrites an expression as a product of brackets or factors — the reverse of expanding.

Factorising explained

Always take out the highest common factor first. Then look for standard patterns: difference of two squares, simple quadratics, and grouping for four-term expressions.
Factorised form is what lets you solve equations quickly, simplify algebraic fractions and find where a graph crosses the axes.

Key formula

x2−a2=(x−a)(x+a)x^{2} - a^{2} = (x - a)(x + a)

Worked example

3x2−12=3(x2−4)=3(x−2)(x+2)3x^{2} - 12 = 3(x^{2} - 4) = 3(x - 2)(x + 2).

Examiner tip

Expand your brackets mentally to check. A ten-second check catches almost every sign error in a factorising question.

Factorising: common questions

How do I factorise a quadratic where a is not 1?
Multiply a by c, find two numbers with that product and a sum of b, split the middle term, then factorise by grouping.
What if an expression will not factorise?
Check the discriminant. If it is not a perfect square the factors are not rational, so use the quadratic formula instead.

Related terms

Quadratic formula

The quadratic formula solves any equation of the form ax² + bx + c = 0, including those that will not factorise.

Completing the square

Completing the square rewrites a quadratic in the form a(x + p)² + q, revealing the turning point and allowing exact solutions.

Practise mathematics on MathsGradeUp

Take factorising from a definition to full marks with exam-board question banks, revision notes and instant step-by-step feedback from Study Coach.

Maths revision notesPractice questionsCreate a free account

Related on MathsGradeUp

Keep studying

Practise it