I'm hoping to complete the exercises in chapter 1.3 Basic Mathematics, Serge Lang.
The section question is:
Expand the following expressions as sums of powers of $\;x\;$ multiplied by integers. These are in fact called polynomials. You might want to read, or at least look at, the section on polynomials later in the book (Chapter 13, §2).
Chapter 13.2 is of no help and I don't understand what the question is asking.
The answer to one expression:
4) $\qquad(2 - 4x)^2$ $\quad$ is $\quad$ $16x^2 - 16x + 4$
I'm lost here. How does it get there?
EDIT: for learning, @Ethan's answer is the most comprehensive, for study/practice, @AWertheim's answer is invaluable (comments also point to distributivity, essential here), chose the answer that most directly answered this question.
Goes upvotes other good answers by these users