Answer the questions based on the following information. A, S, M and D are functions of x and y, and they are defined as follows.

$$A(x, y)=x + y$$

$$S(x, y)=x-y$$

$$M(x, y)=xy$$

$$D(x,y)=\frac{x}{y}$$. $$y\neq0$$

Question 16

What is the value of $$S[M(D(A(a, b), 2), D(A(a, b), 2)), M(D(S(a, b), 2), D(S(a, b), 2))]$$?


Given expression can be reduced to:

$$S[M(\frac{a+b}{2}),(\frac{a+b}{2})), M((\frac{a- b}{2}, (\frac{a-b}{2})]$$

= $$S[(\frac{(a+b)}{2})^2, (\frac{(a-b)}{2})^2]$$

= $$(\frac{a+b}{2})^2 - (\frac{(a-b)}{2})^2 $$

= ab

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