Picture a rectangle that's a tall and (b + c) long. Its area is height × length, so a × (b + c). Nothing new yet — that's just area of a rectangle from last year.
Now Slice It Down the Middle
Draw a line that splits the long side into the b bit and the c bit. You've cut the one rectangle into two smaller ones sitting side by side. The left one is a × b and the right one is a × c. Same rectangle, same total area — you only drew a line. So the whole thing must equal the two pieces added together: a(b + c) = ab + ac. Press "pull the two parts apart" in the toy and you'll literally watch one rectangle become two without any area going missing.
Why "distributive"
To distribute means to share something out. The a gets shared out to the b and the c — every term inside gets a turn being multiplied. Three terms inside? The outside number hits all three. It never just multiplies the first one and stops, and that's the single thing to lock in now.
It Works with Numbers Too
The pieces don't have to be letters. 3 × (4 + 2) is 3 × 6 = 18, and also 3×4 + 3×2 = 12 + 6 = 18 — same answer, because it's the same rectangle. Drag the toy to any numbers you like and the two lines of working always land in the same place. That's not a coincidence; it's the area not caring how you slice it.