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Recognise a complete cube (a +/- b)^3 in an expression

This type of question, asked 3 times: 14 Jul 2023 S4, 12 Sep 2024 S1, 17 Sep 2024 S2. All 3 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S4

    73
    If a=17a = 17, b=13b = 13, then find the value of the expression (a3−b3−3a2b+3ab2)(a^3 - b^3 - 3a^2 b + 3ab^2).

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  2. Question 2

    12 Sep 2024 S1

    60
    Let t=25t = \frac{2}{5}, then the value of the expression t3+(35)3+95tt^3 + \left(\frac{3}{5}\right)^3 + \frac{9}{5}t is:

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  3. Question 3

    17 Sep 2024 S2

    69
    If a3+3a2+3a=7a^3 + 3a^2 + 3a = 7, then the value of a2+2aa^2 + 2a is:

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