Cracking Quadratics: Expand, Recognise, Factorise
1 of 4Maths
Cracking Quadratics: Expand, Recognise, Factorise
For grown-ups
Companion summary
Have you ever watched a ball arc perfectly through the air and wondered what invisible rule it follows? Quadratic expressions describe that curve — engineers use them to design bridges, ramps, and even roller coasters. The expression x squared minus 9 secretly hides two factors: it is the same as (x plus 3)(x minus 3). When you feel confident, try spotting which real-world shapes around you might follow a curved, quadratic path.
Warm-Up: Powers and Pairs
Warm-Up: Powers and Pairs
Here is a quick puzzle. If you multiply (x + 3) by (x + 3), do you think the answer will still look like a simple 'x + something'? Or will something unexpected appear? Before we check, remind yourself of these two ideas: • x² means x multiplied by x. It is called 'x squared'. • When we expand brackets, we multiply every term inside one bracket by every term inside the other. Hold your prediction in your head. By the end of this lesson you will know exactly what comes out — and why it matters.
💭 Think about this
What do you think (x + 2)(x + 5) might equal? Write a guess before we work through it together.