find the polynomial in descending powers of z representing the area of the shaded region. the area of the…

Explanation:

Step1: Find area of large square

The side - length of the large square is (z + 8). The area of a square is (A = s^2), so the area of the large square (A_{1}=(z + 8)^2). Using the formula ((a + b)^2=a^{2}+2ab + b^{2}), where (a = z) and (b = 8), we have (A_{1}=z^{2}+16z + 64).

Step2: Find area of small square

The side - length of the small square is (z). The area of a square is (A = s^2), so the area of the small square (A_{2}=z^{2}).

Step3: Find area of shaded region

The area of the shaded region (A) is the area of the large square minus the area of the small square. So (A=A_{1}-A_{2}=(z^{2}+16z + 64)-z^{2}). Combining like - terms: (z^{2}-z^{2}+16z + 64=16z + 64).

Answer:

(16z + 64)