Factor Difference Squares Worksheets Grade 9

1. A construction company is designing a square plaza with a smaller square fountain removed from one corner. The remaining area for walking space is given by the expression 49x² - 64 square meters. The project manager needs to determine the dimensions of this L-shaped walking area to calculate how much paving material to order. If the longer side of the rectangular walking section measures (7x + 8) meters, what is the width of this rectangular section in terms of x?
2. Liam is designing a rectangular garden with an area that can be expressed as (x² - 16) square meters. He realizes this area represents the difference between the area of the entire garden space and the area of a smaller square patio he plans to remove. If the garden's length is (x + 4) meters, what is its width in terms of x?
3. A physics class is designing a solar panel array where the total area can be expressed as 49x² - 64 square meters. The teacher explains that this represents the difference between the area of the entire mounting surface and the area of a smaller control unit that will be removed. If the array's length is (7x + 8) meters, what expression represents the width of the solar panel array?

…and 4 more problems

1. Emma is designing a square mosaic tile for an art project. The tile is composed of a smaller square of colored glass placed at the center of a larger square frame made of metal. The side length of the entire mosaic (frame plus glass) is (7x + 3) centimeters. The side length of the central glass square is (7x - 3) centimeters. Using the difference of squares, what is the area of just the metal frame in square centimeters?
2. Aisha is designing a solar panel installation for her school's rooftop. The total area available for panels can be expressed as 49x² - 64 square meters. She realizes this area represents the difference between the area of the entire rectangular roof section and the area of a ventilation shaft that needs to remain uncovered. If the length of the roof section is (7x + 8) meters, what expression represents the width of the available installation area?
3. Mason is designing a rectangular garden in his backyard. The area of the garden is represented by the expression 121x² - 100 square feet. He knows that the length of the garden is (11x + 10) feet. If the area of a rectangle is equal to its length times its width, what expression represents the width of Mason's garden in terms of x?

…and 3 more problems

1. Aisha is designing a solar panel array that will cover an area of (49x² - 64) square meters. She realizes this area represents the difference between the total available space and the area needed for maintenance access. If the length of the array is (7x + 8) meters, what expression represents the width of the solar panel array in terms of x?
2. A rectangular garden has an area represented by the expression x² - 16 square meters. If the length of the garden is (x + 4) meters, what is the width of the garden in terms of x?
3. Emma is designing a solar panel installation for her school's rooftop. The total area available for panels can be expressed as (49x² - 64) square meters. She realizes this area represents the difference between the area of the entire rectangular space and the area of a ventilation shaft that will remain uncovered. If the length of the installation area is (7x + 8) meters, what expression represents the width of the installation area in terms of x?

…and 4 more problems