Lab: Area-Model Distributor
Drag the sliders and watch a(b + c) split into ab + ac as areas — distribution you can see.
Area model: 3(x + 4)
a·b
a·c
3(x + 4) = 3x + 12
Try it
Challenge: set a = 4, b = 2, c = 5. What is 4(2x + 5) expanded?
Move the sliders, read the two area labels, then type the expansion (like 8x+20).
What to notice: the whole rectangle’s area never changes — splitting it just reveals the two products hiding inside the parentheses.
Why it works
Area is length × width. A rectangle a units tall and (b + c) units wide has area a(b + c); cutting it at the b|c boundary gives areas ab and ac. Same rectangle, two descriptions — that is the distributive property.