## Multiplication Not Distributive (MND)

In precalculus/algebra we become familiar with the *distributive
laws* that address interactions between multiplication and
addition/subtraction. Specifically, these laws say

We use these laws all the time, both in expanding
and in factoring

We even use it (although we don't often think about it this
way and usually don't include the middle step below) when combining
like terms, as in

The problem is when students misinterpret these laws, thinking they
also say something about interactions between more than one
multiplication; that is, they ``invent" for themselves a law that
looks something like:

This clearly is false, as most would see if these were all numbers
-- few (though I cannot go so far as to say *no one*) would
assert, say, that

But when the objects involved are expressions involving variables,
the error is frequently made, such as in this case:

or

Top Algebra Errors Made by Calculus Students
(full document)

Full List of Grading Codes

Thomas L. Scofield
2003-09-04