Special Products Worksheets Grade 9

1. An architect is designing a rectangular garden with a circular fountain in the center. The garden's area is represented by (4x² + 20x + 25) square meters, while the fountain occupies (4x² - 9) square meters. What expression represents the area of the garden space available for planting flowers, and what is this area in simplified form?
2. An architect is designing a rectangular conference room with dimensions (5x + 8) feet by (5x - 8) feet. The client wants to install acoustic panels that cost $12 per square foot. What simplified algebraic expression represents the total area of the conference room floor?
3. (15x + 12y)(15x - 12y) = ?

…and 5 more problems

1. (6x + 8y)(6x - 8y) = ?
2. Emma is constructing a decorative rectangular frame for a large abstract painting. The length of the frame is (7x + 9) centimeters and the width is (7x - 9) centimeters. She needs to calculate the area of the frame's opening (the space inside the frame) to ensure the painting fits perfectly. What is the simplified expression for the area of the frame's opening in square centimeters?
3. An architect is designing a rectangular conference room where the length is (5x + 8) feet and the width is (5x - 8) feet. To determine the appropriate ventilation system, she needs to calculate the room's area. What is the simplified expression for the area of the conference room in square feet?

…and 4 more problems

1. An architect is designing a rectangular conference room with dimensions (5x + 8) feet by (5x - 8) feet. She needs to calculate the area to determine the flooring requirements. Using the difference of squares formula, what is the simplified expression for the area of the conference room in square feet?
2. (8x + 9y)(8x - 9y) = ?
3. A right triangle is drawn on a coordinate plane with vertices at (0,0), (2x,0), and (0,3x). The hypotenuse has a length of 5√13 units. Using the Pythagorean theorem, determine the value of x.

…and 6 more problems