8.4 Factorising with common factors — Learn

Prerequisites: expanding a single bracket and identifying common factors in integers.

By the end of this section you can: factorise an expression by taking out its common factor and check by expanding.

Covers: A4.

Learn the method

Factorising reverses expanding. It writes a sum as a product.

A common factor divides every term. Find the greatest common numerical factor and any variable shared by all terms.

For $12x+18$, the greatest common factor is $6$: $12x+18=6(2x+3)$.

Check by expanding the bracket. The result must match the original expression.

Worked example. Factorise $15x+20$.

$15x+20=5(3x+4)$ — take out the common factor $5$.

Check: $5(3x+4)=15x+20$.

Watch out. Factorising only the first term leaves the expression unchanged incorrectly. Divide every term by the common factor, then expand your answer to check.

You should now be able to

• factorise an expression by taking out its common factor and check by expanding.