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?

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Solution

Length of one side of the rectangle =

Length of the other side of the rectangle =

Area of the rectangle = Product of the two sides

From the given rectangle, a square of side length (x + y) is removed.

Area of the square = Side × Side = (x + y)² = x² + 2xy + y²

Remaining area = Area of rectangle − Area of square

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