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Instructions
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 $$S[M(D(A(a, b), 2), D(A(a, b), 2)), M(D(S(a, b), 2), D(S(a, b), 2))]$$?
Solution
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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