Visualize the distributive property with an area model for (a + b) x (c + d).
Last updated: June 2026 | By Patchworkr Team
Enter four values to see how the distributive property breaks a rectangle into four parts.
The rectangle is split into four regions that correspond to a x c, a x d, b x c, and b x d.
This geometric picture is the reason the distributive property works for binomial multiplication.
Example: (3 + 2) x (5 + 1) = 30.
Find (3 + 2) x (5 + 1).
1. a = 3, b = 2, c = 5, d = 1
2. ac = 15, ad = 3, bc = 10, bd = 2
3. Sum = 15 + 3 + 10 + 2
Final answer: 30
Can I use negative numbers?
Yes. The model still works because multiplication distributes over signed values.
Can I use decimals?
Yes. The areas will be decimal values, and the total still matches the expanded product.
Why is this useful for algebra?
It shows why multiplying binomials produces four terms instead of two.
Does this only work for positive dimensions?
No. The calculator is a general algebraic model, not a physical rectangle tool.
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