The expression to represent the area of the shaded region in simplest form 14x² - 6x - 2.
To find the expression to represent the area of the shaded region in simplest form, use the formula for calculating the area of a rectangle.
To calculate the area of the bigger rectangle.
Area of Rectangle (Bigger) = Length × Breadth
Given:
Length = 3x - 1
Breadth = 5x + 2
Area of Rectangle (Bigger) = (3x - 1) × (5x + 2)
Area of Rectangle (Bigger) = 15x² + 6x - 5x - 2
Area of Rectangle (Bigger) = 15x² + x - 2
Area of Rectangle (Smaller) = Length × Breadth
Given:
Length = x + 7
Breadth = x
Area of Rectangle (Smaller) = (x + 7) × (x)
Area of Rectangle (Smaller) = x² + 7x
Therefore, area of the shaded part = Area of Rectangle (Bigger) - Area of Rectangle (Smaller)
Area of Shaded Part = (15x² + x - 2) - (x² + 7x)
Area of Shaded Part = 15x² + x -2 - x² - 7x
Area of Shaded Part = 14x² - 6x - 2
Therefore, the expression to represent the area of the shaded region in simplest form is 14x² - 6x - 2.