Q19 of 59 Page 162

The sides of a rectangle are 2x + 3y and 3x + 2y. From this a square of side length x + y is removed. What is the area of the remaining region?

Length of rectangle = 2x + 3y


Breadth of rectangle = 3x + 2y


Area of rectangle = (Length× breadth) = (2x + 3y)× (3x + 2y)


⇒ Area of rectangle = 6x2 + 13xy + 6y2


Side of square = x + y


Area of Square = (Side× Side) = (x + y)2


⇒ Area of Square = x2 + y2 + 2xy


Area of remaining region = ( Area of rectangle- Area of Square) = 5x2 + 5y2 + 11xy


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