ABC26GN0997 · Simplification
Subject: General Aptitude · Chapter: Simplification · Exam: · Marks: · Difficulty:
If $a+b+c=2 s$, then the value of $(s-a)^{2}+(s-b)^{2}$ $+(s-c)^{2}+s^{2}$ will be
(a)$s^{2}-a^{2}-b^{2}-c^{2}$
(b)$s^{2}+a^{2}+b^{2}+c^{2}$
(c)$a^{2}+b^{2}+c^{2}$
(d)$4 s^{2}-a^{2}-b^{2}-c^{2}$
Answer
Explanation
$(s-a)^{2}+(s-b)^{2}+(s-c)^{2}+s^{2}$ $$\begin{aligned} & =\left(s^{2}+a^{2}-2 s a\right)+\left(s^{2}+b^{2}-2 s b\right)+\left(s^{2}+c^{2}-2 s c\right)+s^{2} \\ & =4 s^{2}+\left(a^{2}+b^{2}+c^{2}\right)-2 s(a+b+c) \\ & =(2 s)^{2}+\left(a^{2}+b^{2}+c^{2}\right)-(a+b+c)(a+b+c) \\ & =(a+b+c)^{2}+\left(a^{2}+b^{2}+c^{2}\right)-(a+b+c)^{2} \\ & =a^{2}+b^{2}+c^{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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