4.1 Transforming Expressions

Quite often it is useful to put a mathematical expression into a different form. Perhaps looking at the expression in a different way will lend some critical insight. Mathematica has several functions that can help us do this. In Example 4.1.1, we use the Expand function to multiply out a product and name the result poly.

n[15]:= (* expanding a polynomial *)        <b class="bold">poly = Expand [(1 +x)<sup3</sup> (x -2 y)]</b>Out[15]= x + 3 x<sup2</sup> +3 x<sup3</sup> +x<sup4</sup> -2 y 6 x y - 6 x<sup2</sup> y -2 x<sup3</sup> y

We can perform the opposite of Expand by using the Factor function. In Example 4.1.2, we factor poly and get right back to where we started.

In[16]:= (* factoring a polynomial *)         <b class="bold">Factor [poly]</b>Out[16]= (1 + x)<sup3</sup> (x - 2 y)

Since poly is a polynomial in both x and y, it might be interesting to write it as a polynomial in one variable, with coefficients in the other. We can do this with the Collect function. In general, Collect takes two arguments. The first is the expression that we want to transform and the...