If a 299 b 298 c 297 then the value of 2a3 2b3 2c3 6abc is ........

Quantitative Aptitude (CGL) Algebra

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If a = 299, b = 298, c = 297 then the value of 2a³ + 2b³ + 2c³ - 6abc is

5154

5267

5364

5456

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Explanation:

a = 299, b = 298, c = 297
2a^3+2b^3+2c^3−6abc
= 2(a^3+b^3+c^3−3abc)
= 2(a+b+c)[a^2+b^2+c^2−ab−bc−ca]
= 2×1/2(a+b+c)[(a−b)^2+(b−c)^2+(c−a)^2]
= (a+b+c)[(a−b)^2+(b−c)^2+(c−a)^2]
= (299+298+297)[(299−298)^2+(298−297)^2+(297−299)^2]
= 894×[1+1+4]
= 894×6=5364