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Given x + y + z = 0, use x^3 + y^3 + z^3 = 3xyz to simplify

This type of question, asked 3 times: CDS 1 2018, CDS 1 2021, CDS 2 2026. All 3 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    10
    If x+y+z=0x + y + z = 0, then what is (y+z−x)3+(z+x−y)3+(x+y−z)3(y + z - x)^3 + (z + x - y)^3 + (x + y - z)^3 equal to?

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  2. Question 2

    CDS 1 2021

    7
    If a+b+c=0a + b + c = 0, then which of the following are correct? 1. a3+b3+c3=3abca^3 + b^3 + c^3 = 3abc 2. a2+b2+c2=−2(ab+bc+ca)a^2 + b^2 + c^2 = -2(ab + bc + ca) 3. a3+b3+c3=−3ab(a+b)a^3 + b^3 + c^3 = -3ab(a + b) Select the correct answer using the code given below.

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  3. Question 3

    CDS 2 2026

    35
    If x+y+z=0x + y + z = 0, then what is x(y+z)2+y(z+x)2+z(x+y)2x(y + z)^2 + y(z + x)^2 + z(x + y)^2 equal to ?

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