Exploring Multiplication of Binomials and Polynomials

What is the initial approach to calculate the area of the large rectangle?

• By adding the perimeters of the smaller rectangles

• By using the Pythagorean theorem

• By multiplying the height and width of the large rectangle

• By dividing the large rectangle into smaller squares

How is the height of the large rectangle calculated?

• By adding the heights of the smaller rectangles

• By subtracting the width from the height

• By summing y^2 and -6y

• By multiplying the width by 2

Why can the distance -6y be considered positive?

• Because y is always positive

• Because it is a mathematical error

• Because distances are always positive

• Because -6y can be positive if y is negative

What is the width of the large rectangle?

• 3y^2 - 2y + 1

• y^2 - 6y

• y^2 + 6y

• 3y^2 + 2y - 1

What is the alternative approach to calculate the area of the large rectangle?

• By dividing the large rectangle into four equal parts

• By using the formula for the area of a circle

• By summing the areas of the six smaller rectangles

• By multiplying the height and width of the large rectangle

What is the area of the purple rectangle?

• y^2 * 1

• y^2 * -2y

• y^2 * -6y

• y^2 * 3y^2

What is the area of the yellow rectangle?

• y^2 * -6y

• y^2 * 3y^2

• y^2 * 1

• y^2 * -2y

What is the area of the blue rectangle?

• y^2 * -2y

• y^2 * 3y^2

• y^2 * -6y

• y^2 * 1

What is the area of the green rectangle?

• -6y * y^2

• -6y * 3y^2

• -6y * -2y

• -6y * 1

What is the final simplified expression for the area of the large rectangle?

• 3y^4 - 20y^3 + 13y^2 - 6y

• 3y^4 + 20y^3 - 13y^2 + 6y

• 3y^4 + 20y^3 + 13y^2 - 6y

• 3y^4 - 20y^3 - 13y^2 + 6y