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Given 2s = a + b + c, simplify an expression in s - a, s - b, s - c

This type of question, asked 2 times: CDS 2 2023, CDS 1 2025. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2023

    80
    If 2s=a+b+c2s = a + b + c, then what is s2+(s−a)(s−b)+(s−b)(s−c)+(s−c)(s−a)s^2 + (s - a)(s - b) + (s - b)(s - c) + (s - c)(s - a) equal to ?

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  2. Question 2

    CDS 1 2025

    75
    If 2s=a+b+c2s = a + b + c, then what is s (s−a) (s−b) (s−c)[1s−a+1s−b+1s−c−1s]s\,(s - a)\,(s - b)\,(s - c)\left[\frac{1}{s - a} + \frac{1}{s - b} + \frac{1}{s - c} - \frac{1}{s}\right] equal to ?

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