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.

What is the result when you distribute the terms in the expression (A + B)(C + D)?

• A*B + C*D

• A*D + B*C

• A*C + A*D + B*C + B*D

• A*C + B*D

If a square's side is increased by 15 units, and the original side is 12 units, what is the new side length?

• 24 units

• 30 units

• 27 units

• 25 units

How do you express the area of a new square with side length X + Y using polynomial identities?

• X^2 + 2*X*Y + Y^2

• X*Y + X^2

• X^2 + Y^2

• 2*X*Y

What is the area of a square with an initial side length of 11 increased by 13 units?

• 484

• 576

• 625

• 729

When decreasing the side of a square by 5 units, which part of the polynomial identity changes?

• X^2

• 2*X*Y

• None of the above

• Y^2