An algebra problem by Jyotisman Das
Algebra
Level
2
What is the simplified expression for: (x+y-2z)^{3} + (x-2y+z)^{3} + (y+z-2x)^{3}
(x+y-2z) + (x-2y+z) + (y+z-2x)
(x+y-2z) - (x-2y+z) - (y+z-2x)
(x+y-2z)^{2} - (x-2y+z)^{2} - (y+z-2x)^{2}
3(x+y-2z)(x-2y+z)(y+z-2x)
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Let, (x+y-2z) = a (x-2y+z) = b (y+z-2x) = c Now, we can see that, a +b + c = 0 Therefore, a^3 + b^3 + c^3 = 3abc {Fundamental operation}
Hence, correct answer is 3abc = 3(x+y-2z)(x-2y+z)(y+z-2x).]