Chapter 8: Algebraic expressions and manipulation

The chapter problem: a rectangular frame

A maker builds a rectangular frame. Its outer sides measure $x+6$ cm and $x+4$ cm. The opening measures $x$ cm by $x+2$ cm.

First contact: without working it out, predict whether the frame area is closer to $10x$ or $12x$ square centimetres when $x$ is large. You can change your prediction later. The frame area is the outer area minus the opening area.

By the end, you will find a simplified expression for the frame area and calculate it for a chosen value of $x$.

By the end of this chapter you will be able to

• use algebraic notation and name variables, terms, coefficients and constants;
• simplify expressions by collecting like terms;
• expand brackets and factorise using common factors;
• substitute values into expressions and formulae;
• rearrange formulae to change the subject;
• expand a product of three binomials (Higher only).

Roadmap

1. 8.1 Algebraic notation and vocabulary
2. 8.2 Simplifying and collecting like terms
3. 8.3 Expanding brackets
4. 8.4 Factorising with common factors
5. 8.5 Substitution into expressions and formulae
6. 8.6 Rearranging formulae
7. 8.7 Expanding products of three binomials (Higher only)
8. Review

Your turn to connect it

Where might you use a formula or a letter to describe an unknown amount? Give one example from your own life, then say what each letter could represent.