Expanding & Factorising

Overview

Expanding means multiplying out a bracket, and factorising is the reverse — putting an expression back into a bracket by taking out a common factor. In Year 8 students learn to expand single brackets such as 3(x + 4) and to factorise expressions such as 6x + 9. These two skills are opposites of each other and are used in almost every algebra question from here on.

What You Will Learn

• Expand a single bracket such as 4(x + 3)
• Expand brackets with negative terms, such as 2(3x − 5)
• Simplify expressions by expanding and then collecting like terms
• Factorise an expression by taking out the highest common factor
• Check a factorised answer by expanding it again

Key Vocabulary

Common Mistakes to Avoid

• Only multiplying the first term inside the bracket, e.g. 3(x + 4) = 3x + 4 instead of 3x + 12
• Getting the sign wrong when expanding a negative, e.g. −2(x − 3) = −2x − 6 instead of −2x + 6
• Not taking out the highest common factor, e.g. writing 2(3x + 6) instead of fully factorising 6x + 12 as 6(x + 2)
• Forgetting the 1 when a term is fully divided, e.g. factorising 5x + 5 as 5(x) instead of 5(x + 1)

Frequently Asked Questions