Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

The Distributive Law

Quite likely the greatest source of errors in Intermediate Algebra is the Distributive Law

$\displaystyle a(b+c ) = ab + ac. $

Since the commutative Law

$\displaystyle uv = vu $

also holds we have the alternative version

$\displaystyle (b+c)a = ba + ca = ab + ac. $

There are several subtleties in this law, any of which can give rise to errors.

You should work through all of the following items and make sure you understand what they say. If it helps assign values to the variables, such as

$\displaystyle a=2, \quad b=3, \quad c= 5. $

Also consider the special cases that some of the variables are $ 0 $, or $ 1 $, or negative.