Final answer:
The expressions are as follows: a) 3X + Y, b) A² + 2B + C, c) ((A + B) / (C - D)) * (X / Y), d) ((A² + 2B + C) / D) / (XY).
Step-by-step explanation:
a. The expression 3X + Y represents the result of multiplying X by 3 and adding Y to it. For example, if X = 2 and Y = 4, the expression would evaluate to 3(2) + 4 = 10.
b. The expression A² + 2B + C represents the sum of the square of A, the result of multiplying B by 2, and C. For example, if A = 3, B = 5, and C = 1, the expression would evaluate to 3² + 2(5) + 1 = 23.
c. The expression ((A + B) / (C - D)) * (X / Y) represents the result of adding A and B, subtracting D from C, dividing the sum by the difference, dividing X by Y, and multiplying the two results together.
For example, if A = 2, B = 3, C = 6, D = 2, X = 4, and Y = 2, the expression would evaluate to ((2 + 3) / (6 - 2)) * (4 / 2) = (5 / 4) * 2 = 2.5 * 2 = 5.
d. The expression ((A² + 2B + C) / D) / (XY) represents the result of summing the square of A, 2 times B, and C, then dividing the sum by D, and finally dividing the result by the product of X and Y.
For example, if A = 4, B = 2, C = 3, D = 5, X = 2, and Y = 3, the expression would evaluate to ((4² + 2(2) + 3) / 5) / (2(3)) = (16 + 4 + 3) / 5 / 6 = 23 / 5 / 6 = 0.7667.