Updated October 29, 2008
1. First, a basic definition: saying that two monomials
are relatively prime means that they have no common factor.
For instance, in 3 variables, xy and xz are not relatively prime because y is a common factor. On the other hand,
xy and z² are relatively prime.
2. Now a question: if two monomials are relatively prime,
what is their LCM? Similar terminology is used for integers.
For instance, 6 and 25 are relatively prime: what is their LCM? A very similar answer is valid for relatively prime monomials.
3. The equation that you're asked to prove in part a
certainly is true, but something slightly different may be more useful in
First, note that fg is both added and subtracted in the expression on the right side. Therefore, that equation is equivalent to
the following equation:
Comments and questions to: email@example.com
Back to the homework list.