Factor Difference Squares Worksheets Grade 9

1. x⁴ - 81 = ?
2. A square painting is mounted on a square frame, creating a border of uniform width around the painting. The entire artwork (painting plus frame) has side length (x + 6) inches, while the painting itself has side length (x - 6) inches. Using the difference of squares, what is the area of just the frame in square inches?
3. A construction company is designing a square plaza with a smaller square fountain in the center. The total area available for the plaza is (9x² - 16) square meters. The fountain will occupy an area that can be expressed as a perfect square. If the side length of the fountain is (3x - 4) meters, what is the side length of the entire plaza in terms of x?

…and 4 more problems

1. x² - 81 = ?
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. Liam is designing a rectangular garden with an area that can be expressed as (16x² - 81) square feet. He realizes this area represents a difference of two perfect squares. What are the dimensions (length and width) of Liam's garden, expressed as binomial factors?

…and 5 more problems

1. Emma is designing a square mosaic for her art project. She starts with a large square tile of area (9x² - 16y²) square inches. She realizes this area represents the difference between the area of the original tile and a smaller square section she plans to remove. If the side length of the original tile is (3x + 4y) inches, what expression represents the side length of the smaller square section in inches?
2. 49x² - 81y² = ?
3. Emma is designing a solar panel array for her school's science fair project. The total area available for the panels can be expressed as 49x² - 64 square meters. She realizes this area represents the difference between the area of the entire roof space and the area where panels cannot be installed. If the length of the available space is (7x + 8) meters, what expression represents the width of the available space in terms of x?

…and 4 more problems