**This is the students’ version of the page. Log in above for the teachers’ version.**

- A1a – Using and interpreting algebraic notation
- A2a – Substituting numerical values into formulae and expressions
- A4a – Simplifying and manipulating algebraic expressions by collecting like terms (basic)
- A4b – Multiplying a single term over a bracket
- A4c – Factorising (basic)
- A4d – Multiplying two or more brackets

# Factorising quadratics

- Fully factorise \(x^4-1\)

- Define \(u = x^2\). Then \(u^2=x^4\).

- \(x^4-1 \equiv u^2-1 \equiv (u+1)(u-1) \equiv (x^2+1)(x^2-1) \equiv (x^2+1)(x+1)(x-1)\)

- Expand \((x+\frac{1}{2})(x+6)\). Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?
- Expand \((x+\frac{1}{2})(2x+6)\). Is it possible factorise this expanded expression so that the factors only contain integer coefficients and constants?

- \((x+\frac{1}{2})(x+6)\equiv x^2+\frac{13}{2}x+3\); no
- \((x+\frac{1}{2})(2x+6)\equiv 2x^2+7x+3 \equiv (2x+1)(x+3)\)

Stan and Ollie are trying to factorise \(x^2-5x+6\). Stan writes \((x-2)(x-3)\). Ollie writes \((2-x)(3-x)\). Are either of them correct? If so, who?

Hover for answers:

- They’re both correct, but Stan’s factorisation is more conventional.

### Factorising non-monic quadratic expressions

Click the “New question” to generate a new expression to factorise. Drag down the slider for a step-by-step solution using the grouping method. Note that the applet will occasionally generate an expression that can be factorised easily by a different method (e.g. completing the square) to help you practise those skills. In these cases, the slider is replaced with a simple button to reveal the answer.

**Teachers**: log in to access the following:

- Worksheet (with space for student work)
- Handout (slides with exercises only; 4 per page for reduced printing)

- Skills drill worksheet (40 questions on one side of A4; answers included)

**Teachers**: log in to access these.

*In the real world*‘ section for that lesson shows why quadratics are so relevant in the real world.