Multiplication and Division Activities

When you approach situations in which you must divide one polynomial by another, grouping like terms allows you to use the properties of exponents more readily. Often, such work begins with expressions or terms that involve combinations of positive and negative exponents. Here is such an expression.

In each step above, you avoid most of the complexity the division might involve by rearranging the expression so that you can carry out the divisions using exponential arithmetic.

Here is another expression that involves exponents. In this instance, the numerator contains a binomial that you approach by making the denominator explicit for each of the terms in the binomial.

Here is another problem that appears involved until you rearrange its terms so that you can view them in relative isolation:

To work with this problem, you proceed in two distinct phases. For the first phase, you group like terms and carry out the multiplications. For the second phase, you again group like terms, but this time you carry out the divisions.