Proving the Relationship between Side Length and Area of a Square

The video tutorial explains how to prove patterns in relationships by squaring the sum of two terms. It covers the process of distributing terms, simplifying expressions, and understanding polynomial identities. The tutorial demonstrates how to calculate the area of a square when its sides are increased or decreased by a certain amount, using polynomial identities to describe these changes. Examples are provided to illustrate the concepts, and the video concludes with a discussion on how decreasing side lengths affect polynomial identities.

Explain how to test a polynomial identity using specific values for the side lengths.

What happens to the area of a square when its sides are decreased by a certain amount?