Find a simplified expression for the area of the shaded region below

Area of the shaded region = (8x + 6)

Step-by-step explanation:

Area of the shaded region = Area of the large rectangle - Area of the smaller rectangle

Area of the large rectangle = Length × width

                                             = (x + 3)(x + 2)

                                             = x(x + 2) + 3(x + 2)

                                             = x² + 2x + 3x + 6

                                             = x² + 5x + 6

Area of the smaller rectangle = x(x - 3)

                                                 = (x² - 3x)

Area of the shaded region = (x² + 5x + 6) - (x² - 3x)

                                            = x² + 5x + 6 - x² + 3x

                                            = (8x + 6)

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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