Find the value of \( \Large a^{3} + b^{3} + c^{3} - 3abc \) when a = 225, b = 226, c = 227

A) 2304

B) 2430

C) 2034

D) 2340

Correct Answer:
C) 2034

Description for Correct answer:

We know that, \( \Large a^{3} + b^{3} + c^{3} - 3abc \)

= \( \Large \left(a+b+c\right)\frac{1}{2} \left[ \left(a-b\right)^{2} + \left(b-c\right)^{2} + \left(c-a\right)^{2} \right] \)

= \( \Large \left(225 + 226 + 227\right)\frac{1}{2}\left[ 1 + 1 + 4 \right] \)

= \( \Large 678 \times 3 = 2034 \)




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