Split a number into two parts to make an expression in them greatest or least

This type of question, asked 4 times: 4 May 2023 S1, 9 May 2024 S1, 20 Apr 2025 S1, 17 Apr 2026 S1. All 4 questions below, oldest first.

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Question 1
4 May 2023 S1
142 $If sum of two numbers is 3, then the maximum value of the product of first number and square of the second number is$
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Question 2
9 May 2024 S1
128 $xy$
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Question 3
20 Apr 2025 S1
103 $20 is divided into two parts so that the product of the cube of one part and the square of the other part is maximum, then these two parts are$
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Question 4
17 Apr 2026 S1
78 $The number 28 is divided into two positive parts such that the sum of the cube of one part and the square of the other part is minimum, then the absolute difference between the two parts is$
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Question 1