(a-b)的3次方+(b-c)的3次方-(a-c)的3次方因式分解
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(a-b)^3+(b-c)^3-(a-c)^3
=(a-b)^3+[ (b-c)-(a-c)] [(b-c)^2+ (b-c)(a-c)+ (a-c)^2 ]
=(a-b)^3-(a-b)[(b-c)^2+ (b-c)(a-c)+ (a-c)^2 ]
=(a-b)^3-(a-b)[(b-c)^2-2 (b-c)(a-c)+ (a-c)^2 +3(b-c)(a-c)]
=(a-b)^3-(a-b)[(b-c)^2-2 (b-c)(a-c)+ (a-c)^2 ]+3(a-b)(b-c)(a-c)
=(a-b)^3-(a-b)[(a-c)-(b-c)]^2+3(a-b)(b-c)(a-c)
=(a-b)^3-(a-b)^3+3(a-b)(b-c)(a-c)
=3(a-b)(b-c)(a-c)
=(a-b)^3+[ (b-c)-(a-c)] [(b-c)^2+ (b-c)(a-c)+ (a-c)^2 ]
=(a-b)^3-(a-b)[(b-c)^2+ (b-c)(a-c)+ (a-c)^2 ]
=(a-b)^3-(a-b)[(b-c)^2-2 (b-c)(a-c)+ (a-c)^2 +3(b-c)(a-c)]
=(a-b)^3-(a-b)[(b-c)^2-2 (b-c)(a-c)+ (a-c)^2 ]+3(a-b)(b-c)(a-c)
=(a-b)^3-(a-b)[(a-c)-(b-c)]^2+3(a-b)(b-c)(a-c)
=(a-b)^3-(a-b)^3+3(a-b)(b-c)(a-c)
=3(a-b)(b-c)(a-c)
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