Perfect Square Trinomials Worksheets Grade 9

1. Mason is building a square-shaped platform for a stage production. The area of the platform (in square meters) is given by the expression 49x² + 28x + 4. Recognizing this as a perfect square trinomial, Mason wants to factor it to find the binomial expression representing the side length of the platform. What is the factored form of the expression?
2. Factor: 9x² - 30x + 25 = ?
3. Factor: 49x² + 112x + 64 = ?

…and 5 more problems

1. A robotics team is designing a square-shaped solar panel for their competition robot. The area of the panel can be expressed as the trinomial 9x² + 30x + 25 square centimeters. If the side length of the square panel is represented by a binomial expression (ax + b), find the exact dimensions of the solar panel.
2. Factor: x² - 14x + 49 = ?
3. Isabella is a landscape architect designing a square-shaped community garden. The area of the garden is given by the perfect square trinomial 49x² + 84x + 36 square meters, where x represents a variable length in meters related to the garden's design. Isabella needs to factor this expression to find the binomial that represents the side length of the square garden. What is the factored form of 49x² + 84x + 36?

…and 4 more problems

1. Liam is designing a rectangular garden with an area that can be expressed as the trinomial x² + 14x + 49 square feet. He realizes this area represents a perfect square. What is the factored form of this expression, which would give the side length of the square garden?
2. A square garden has an area represented by the expression 4x² + 20x + 25 square meters. If the garden's side length is expressed as (ax + b) meters, where a and b are positive integers, what is the factored form that represents the side length?
3. A square mosaic is being designed for a community center. The total number of small colored tiles needed to create the mosaic is given by the expression 4x² + 20x + 25, where x represents the number of tiles along one edge of a smaller decorative border. If the mosaic forms a perfect square arrangement, what is the factored form that represents the side length of the complete mosaic in terms of x?

…and 4 more problems