Expanding, Factorising and Quadratics Topic Review summary

Key learning points

• Expand carefully; watch double signs with negatives.
• Factorise common factors first, then quadratics into brackets when possible.
• Completing the square: $x^2+bx=(x+\frac{b}{2})^2-(\frac{b}{2})^2$.
• Quadratic formula $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$; discriminant classifies roots.
• Sketch using vertex (completed square) and intercepts.

Worked example 1 — Factorise

Solve $x^2-5x+6=0$.

Working

Factorising is fastest here.

Worked example 2 — Complete square

Write $x^2+6x+2$ in completed-square form.

Working

Vertex at $(-3,-7)$.

Worked example 3 — Expand carefully; watch double signs with

Apply this idea from the Topic Review: Expand carefully; watch double signs with negatives.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Factorise common factors first, then quadr

Apply this idea from the Topic Review: Factorise common factors first, then quadratics into brackets when possible.

Working

Attempt without notes, then check the answers PDF.

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.