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The area of the shaded region is the space occupied by the shaded region
The area of the shaded region is [tex]5x^2+7x-26[/tex]
The dimension of the big rectangle is 3x - 4 by 2x + 2.
So, the area of the big rectangle is:
[tex]A_1 = (3x - 4)(2x + 2)[/tex]
Multiply
[tex]A_1 =x^2 -9x + 18[/tex]
The dimension of the small rectangle is x - 3 by x - 6
So, the area of the small rectangle is:
[tex]A_2 =(x - 3)(x - 6)[/tex]
Multiply
[tex]A_2 = x^2 - 9x +18[/tex]
The area of the shaded region is the difference between the above areas.
So, we have:
[tex]A = 6x^2 - x^2-2x+9x-18-8[/tex]
Evaluate the like terms
[tex]A = 5x^2+7x-26[/tex]
Hence, the area of the shaded region is [tex]5x^2+7x-26[/tex]
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