Factorisation: common factors and grouping

2026-10-11Algebraic Manipulation Ms Chu

Take out the highest common factor and factor by grouping before attempting harder patterns.

Key formulas

ax + ay = a(x + y)

ax + bx + ay + by = (a + b)(x + y)

Highest common factor

Find the largest factor common to every term — including numerical coefficients and powers of variables. Factor out completely: 6x²y + 9xy² = 3xy(2x + 3y).

Factorisation by grouping

With four terms, group into two pairs, factor each pair, then factor the common binomial. Rearrange terms if the first grouping fails.

Check by expansion

Always expand your factors mentally to recover the original expression. Missing a sign is the most common error.

Exam habit

Write the HCF clearly above the expression before factoring it out.

Worked example

Factor with HCF

Problem. Factorise 6x²y − 15xy².

Solution. HCF = 3xy. Result: 3xy(2x − 5y).

Review quiz

1 / 4

Factorise 12x + 18

Practice questions

Factorise 12x + 18.
Factorise 4x²y − 10xy².
Factorise x³ + 2x² + 3x + 6 by grouping.

Study notes

Should I factor numbers and variables together?

Yes — pull out the full HCF in one step.

What if grouping fails?

Try a different pairing or check whether a common factor was missed first.