You already know how to expand: a(b + c) = ab + ac. You multiply the a through the bracket. Factorising is the exact same picture, walked backwards — you start with ab + ac and put the bracket back, pulling the shared a out the front.
The Rectangle, Rebuilt
Think of the area model. A rectangle with height a split into two strips — one b wide, one c wide — has two areas: ab and ac. That's the expanded form. But it was always one rectangle, height a, total width b + c. Glue the strips back together and the area is a(b + c). In the toy, press "pull them together" — the two pieces slide into one rectangle and the shared height a pops out the front of a single bracket. That's factorising.
It's the Same Skill, Just the Other Direction
This matters because it means you can always check yourself. Factorise something, then expand your answer back out — if you don't land on what you started with, you've slipped somewhere. Try it with the toy's worked pairs: 3x + 6 becomes 3(x + 2), and expanding 3(x + 2) takes you right back to 3x + 6. A perfect round trip.
Why Bother Going Backwards?
Because the factorised form is tidier and far more useful. a(b + c) shows you the shared structure at a glance — it's the form that simplifies algebraic fractions, and it's the form you'll need to solve equations like x² + 3x = 0 next year. Get comfortable seeing the reverse now, and that later work is barely new.