Expanding and Factorising summary

Key learning points

• Distribute to every term; for double brackets form all four products.
• Take out a common factor first when factorising.
• Check by expanding your factors.
• Difference of squares: $a^2-b^2=(a-b)(a+b)$.

Worked example 1 — Expand

Expand $(2x-1)(x+4)$.

Working

Collect the middle terms $-x+8x$ carefully.

Worked example 2 — Distribute to every term; for double brackets form

Use this method from the Expanding and Factorising sheet: Distribute to every term; for double brackets form all four products.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 3 — Take out a common factor first when factorising

Use this method from the Expanding and Factorising sheet: Take out a common factor first when factorising.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 4 — Check by expanding your factors

Use this method from the Expanding and Factorising sheet: Check by expanding your factors.

Working

Each key learning point matches a question type on the printable worksheet.

Worked example 5 — Difference of squares

Use this method from the Expanding and Factorising sheet: Difference of squares: $a^2-b^2=(a-b)(a+b)$.

Working

Each key learning point matches a question type on the printable worksheet.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.