Distributive Property

The distributive property states that:

a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c)

The distributive property can be visualized as follows:

The width of the orange rectangle is b and the height is a. Thus the area of the orange rectangle is

a ⋅ b

The width of the blue rectangle is c and the height is a. Thus the area of the blue rectangle is

a ⋅ c

Then the total area is

a ⋅ b + a ⋅ c

Since the height of both rectangles is a, we can make a larger rectangle by placing the rectangles side by side. The width of the larger rectangle is b + c, and the height is a. Thus the area of this rectangle is

a ⋅ (b + c)

The two areas are equal. In other words,

a ⋅ (b + c) = (a ⋅ b) + (a ⋅ c)

Here are some examples:

3 ⋅ (4 + 5) = (3 ⋅ 4) + (3 ⋅ 5)

10 ⋅ (2 + 21) = (10 ⋅ 2) + (10 ⋅ 21)

(x / y) ⋅ (m + n) = ((x / y) ⋅ m) + ((x / y) ⋅ n)

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