30 8
+------------------------------------------------------------+-------------------+
I I I
2 I 2 * 30 I 2 * 8 I
I I I
+------------------------------------------------------------+-------------------+
The entire large rectangle above is 38 units long and 2 units wide.
Its area is length times width, so the area is 2 * 38.
38 is also the same as 30 + 8, so the area can also be written as 2(30 + 8).
The left rectangle is 30 units long and 2 units wide. Its area is 2 * 30.
The right rectangle is 2 units long and 8 units wide. Its area is 2 * 8.
If you add the areas of the small rectangles, you get
2 * 30 + 2 * 8
If you add the two small areas, you get the area of the laerge rectangle, so
2(30 + 8) = 2 * 30 + 2 * 8
which is an example of the distributive property.
