упростить (а-b)^3+(b-c)^3+(a-c)^3...

slonic89 @slonic89

August 2021 1 21 Report

упростить (а-b)^3+(b-c)^3+(a-c)^3

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Wani4kaa (a - b)^3 + (b - c)^3 + (a - c)^3 = (a - b + b - c)((a - b)^2 - (a - b)(b - c) + (b - c)^2) + (a - c)^3 = (a - c)(a^2 - 2ab + b^2 - ab + b^2 + ac - bc + b^2 - 2bc + c^2) + (a - c)^3 = (a - c)(a^2 - 3ab + 3b^2 + ac - 3bc) + (a - c)^3 = (a - c)(a^2 - 3ab + 3b^2 + ac - 3bc + (a - c)^2) = (a - c)(a^2 - 3ab + 3b^2 + ac - 3bc + a^2 - 2ac + c^2) = (a - c)(2a^2 - 3ab + 3b^2 - ac + 3bc + c^2) = (a - c)(2a^2 - 3b(a - b - c) - ac + c^2)

(a - c)(2a^2 - 3b(a - b - c) - ac + c^2)

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