Final answer:
To complete the expression x² to make it a difference of two squares, a term b² must be found that can be subtracted from x² such as x² - 1² or x² - 4, leading to factors (x + b)(x - b).
Step-by-step explanation:
To complete the expression to make it a difference of two squares, the given expression x² needs to be paired with a term that when squared can be subtracted from x² to form a zero. The difference of two squares is a pattern in algebra which is written in the form a² - b², where both a and b are nonzero terms. Therefore, for the expression x² to become a difference of two squares, we need to find a term b such that x² can be written as x² - b². This would give us (x + b)(x - b) upon factoring.
For instance, if we have x² - 1, the term 1 is also a square (since 1 = 1²), and thus, we have a difference of two squares: x² - 1², which factors to (x + 1)(x - 1). Similarly, if we encounter x² - 4, the 4 is the square of 2, and we have x² - 2², which factors to (x + 2)(x - 2).
Squaring of exponentials, such as when squaring a term like (a^x), means you would multiply the exponent x by 2, making it (a^x)² = a^(2x).