The expression (q^k - 1)(q^k-1) represents a mathematical product involving powers of a variable q. Here, k is a positive integer, and q can be any number. The term q^k - 1 indicates the difference between q raised to the power of k and 1, while q^k-1 is q raised to one less than k. This expression can be useful in various areas of mathematics, including algebra and number theory. It often appears in the context of polynomial factorization and can help in simplifying equations or finding roots. Understanding such expressions is essential for studying topics like polynomials and exponential functions.