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Given a sum or difference (or sum of squares) and the product: value of a cube sum or difference

This type of question, asked 3 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 8 Aug 2022 Tier II. All 4 questions below, oldest first.

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  1. Question 1

    15 Nov 2020 Tier II

    28
    If 9x2+y2=379x^2 + y^2 = 37 and xy=2xy = 2, x,y>0x, y > 0, then the value of (27x3+y3)(27x^3 + y^3) is:

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  2. Question 2

    29 Jan 2022 Tier II

    18
    If 2x−y=22x - y = 2 and xy=32xy = \frac{3}{2}, then what is the value of x3−y38x^3 - \frac{y^3}{8}?

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  3. Question 3

    29 Jan 2022 Tier II

    82
    If a+b=8a + b = 8, ab=10ab = 10, then the value of a3+b3a^3 + b^3 is:

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  4. Question 4

    8 Aug 2022 Tier II

    38
    If a + b = 6 and ab = 5, then what is the value of a3+b3a^3 + b^3?

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