Special Products Worksheets Grade 9

1. 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?
2. (7x + 2y)(7x - 2y) = ?
3. A rectangular garden has a length of (3x + 5) meters and a width of (3x - 5) meters. The owner wants to install a stone pathway around the perimeter that requires knowing the exact area of the garden bed. What is the area of the garden in simplified form?

…and 5 more problems

1. (3x + 5)(3x - 5) = ?
2. 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.
3. (6x + 8y)(6x - 8y) = ?

…and 5 more problems

1. An engineer is designing a solar panel array that will be installed on a rectangular section of a rooftop. The array's dimensions are represented by (5x + 8) meters in length and (5x - 8) meters in width. To calculate the total power output, she needs to determine the area of the array. What is the simplified expression for the area of the solar panel array in square meters?
2. (9x² - 16y⁴) = ?
3. A rectangular prism has dimensions (2x + 3) cm by (2x - 3) cm by (x + 4) cm. Using the difference of squares pattern, find the volume of the prism as a simplified polynomial expression in terms of x.

…and 5 more problems