This week’s Express is an oldie but a goodie:
Multiplying polynomials can be challenging work. But every once in a while, there’s an expansion that is particularly elegant. One of my favorites is the following expression:
(x−a)(x−b)(x−c)…(x−z)
The ellipsis indicates that every letter is subtracted at some point. If you multiply all these binomials together, can you write the expansion in simplest form?2
The expression contains (x−x). Thus, the entire product is 0.