Finding Dimensions of Figures Formed by Removing Squares

This video tutorial explains how to find the dimensions of a figure formed by the difference between two squares using polynomial identities. It covers the concept of polynomial identities, demonstrates multiplying binomials, and provides examples of calculating dimensions using the difference of squares. The tutorial also addresses handling unknown dimensions and forming rectangles, emphasizing the use of polynomial identities to verify dimensions.

What is a polynomial identity?

• An equation that is never true

• An equation that is true for some values of the variable

• An equation that is true only for positive values

• An equation that is true for all values of the variable

In the example with 81 and 64 square units, what are the dimensions of the resulting rectangle?

• 17 by 1

• 1 by 17

• 9 by 8

• 8 by 9

How do you find the dimensions of a rectangle formed by removing a square Y units on each side from a square X units on a side?

• X * Y and X / Y

• X / Y and X * Y

• X - Y and X + Y

• X + Y and X - Y

What is the polynomial identity for the expression 4 * X^2 - 9?

• (X + 3)(X - 3)

• (2 * X - 3)(2 * X + 3)

• (2 * X + 3)(2 * X - 3)

• (X - 3)(X + 3)

If you start with 81 small squares of side length X and remove 16 squares of side length Y, what are the dimensions of the resulting rectangle?

• 9X + 4Y and 9X - 4Y

• 4X - 9Y and 4X + 9Y

• 9X - 4Y and 9X + 4Y

• 4X + 9Y and 4X - 9Y

What is the side length of the square formed by 16 * y^2?

• 5 * y

• 4 * y

• 3 * y

• 2 * y

What is the polynomial identity for the expression 81 * X^2 - 16 * y^2?

• (4X + 9Y)(4X - 9Y)

• (4X - 9Y)(4X + 9Y)

• (9X - 4Y)(9X + 4Y)

• (9X + 4Y)(9X - 4Y)