To solve , first recognize that the expression inside the brackets represents a difference of squares:

Now, squaring this result gives us:

Thus, we get the coefficients and , leading us to the final result:

The equation encapsulates the elegance of polynomial identities. Historically, polynomial multiplication methods have been utilized since ancient times; Archimedes and other mathematicians began exploring the properties of polynomials long before they were formally defined. These identities show how structured algebra can help simplify complex calculations.

Polynomials are not just academic exercises—they show up in real-world applications too! For example, when modeling physical phenomena, engineers use polynomials to approximate trajectories of objects, or calculate forces in structures. Understanding how to manipulate these expressions can help in engineering, economics, and even computer graphics!