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a +/- b and ab (or the cube sum) given: find a^3 +/- b^3 or the reverse

This type of question, asked 4 times: 27 Jul 2023 S1, 18 Sep 2024 S3, 26 Sep 2024 S2, 19 Sep 2025 S2. All 5 questions below, oldest first.

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  1. Question 1

    27 Jul 2023 S1

    55
    If x+y=25x + y = 25 and xy=20xy = 20, then find the value of x3+y3x^3 + y^3.

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  2. Question 2

    27 Jul 2023 S1

    53
    If 2x+3y=162x + 3y = 16 and xy=9xy = 9, then find 8x3+27y38x^3 + 27y^3.

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  3. Question 3

    18 Sep 2024 S3

    60
    If 3a+2b=273a + 2b = 27 and 27a3+8b3=145827a^3 + 8b^3 = 1458, then find 2ab2ab.

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  4. Question 4

    26 Sep 2024 S2

    62
    If 2a−b=32a - b = 3 and 8a3−b3=9998a^3 - b^3 = 999, then find the value of 4a2−b24a^2 - b^2.

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  5. Question 5

    19 Sep 2025 S2

    57
    If a3+b3=35a^3 + b^3=35 and ab=6ab = 6, find the value of a+ba + b.

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