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Express the area of the shaded region in the room shown algebraically

Express the area of the shaded region in the room shown algebraically-example-1

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to find the shaded area you have to subtract the unshaded small rectangles area from the larger rectangles total area

the larger rectangles area (L) is found by multiplying base by height:
(x+3) • 2x = 2x^2 + 6x

the smaller rectangles area (S) is also found by multiplying base by height:
x • 5 = 5x

then to find the unshaded area take the largest rectangle area and subtract the smaller rectangle (L-S):
2x^2 + 6x - 5x = 2x^2 + x

answer: 2x^2 + x
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