Here is a rectangle with sides a and b+c.
We see that the area is a(b+c). The area is also the sum of the areas of
the two smaller rectangles: ab+ac. So the distributive law seems to be
fairly obvious, when considered geometrically. Return to my Mathematics pages
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The Distributive Law, one of the basic laws of algebra, says: a(b+c)=ab+ac. This is handy for simplifying, by getting rid of parentheses. Factoring an expression like ab+ac=a(b+c) is the distributive law backwards. It too can help to simplify, as maybe the a or b+c can be divided out of a bigger equation somehow.
Here is a rectangle with sides a and b+c.
We see that the area is a(b+c). The area is also the sum of the areas of
the two smaller rectangles: ab+ac. So the distributive law seems to be
fairly obvious, when considered geometrically.
Comment: In Boolean Algebras, we also have a second distributive law: a+bc=(a+b)(a+c). This one doesn't work with numbers.