Question

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Answer 1

The shaded region's area is x² + 23x + 49.

Step-by-step explanation:

Step 1; To calculate the area of the shaded region, we subtract the area of the square which has side lengths of (x + 1) from the entire rectangle. So we determine the equations that denote the areas of the two shapes.

Step 2; Area of the square = side length × side length (x + 1)×(x + 1)    = x² + x + x + 1 = x² + 2x + 1

Area of the bigger rectangle = length × breadth = (x + 10) × (2x + 5)                            = 2x² + 5x + 20x + 50 = 2x² + 25x + 50.

Step 3; The given shaded region's area = Area of the bigger rectangle - Area of the smaller square = 2x² - x² + 25x - 2x + 50 - 1                          = x² + 23x + 49.

So the shaded region's area of x² + 23x + 49.