Answer:
option A : 7x - 1
Explanation:
Area of the shaded region = [ Area of bigger rectangle] - [Area of smaller rectangle ]
Therefore, Area of bigger rectangle = length * breadth = (x - 1)(x + 5)
Therefore, Area of smaller rectangle = length * breadth = (x + 1)(x - 4)
Area of shaded region = [(x - 1)(x + 5)] - [(x + 1) ( x - 4)
= [x(x + 5) - 1(x + 5)] - [x(x - 4) + 1( x - 4)]
= [ x^2 + 5x - 1x -5] - [ x^2 - 4x + 1x - 4]
= x^2 + 5x - 1x - 5 - x^2 + 4x - 1x + 4 ....(after removing the brackets)
= x^2 - x^2 + 5x + 4x - 1x - 1x - 5 + 4.....( as (+ x^2 )and (- x^2 )get eliminated due to opposite signs)
= 9x - 2x - 1
= 7x - 1
So, option A: 7x - 1 is the correct answer.