how do you write a polynomial to represent the area of each shaded region ?

it has the base A and the Height is B.it is 4 unshaded corners there a x on the base and height of the unshaded corner and it is a rectangle  

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Without the unshaded corners the area would be AB. Each of the 4 unshaded corners is a square of area x2, so the total area of the unshaded corners is 4x2 and the total area of the shaded figure is AB-4x2.

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