I am working through Gallian's book "Contemporary Abstract Algebra" (Fifth Edition) and I am on Chapter 20 - Extension Fields.

I need help with Example 1 on page 345 - see attached pdf. [My text below is on the pdf - I am trying to understand the equations]

Example 1 states:

Let

Then in we have

Can someone please help me understand how the above two lines are equal?

Could you also explain how the last two eqations of the 4 are equal - see attached sheet.

Bernhard