Câu hỏi của Cold Heart

Question

Phân tích thành nhân tử:a)$a^2\left(a-b\right)-b^2\left(a-c\right)-c^2\left(b-a\right)$b)$a\left(b-c\right)^3+b\left(c-a\right)^3+c\left(a-b\right)^3$c) \(abc-\left(ab+ac+bc\right)+\left(a+b+c\rig...

Bùi Hồng Anh · Accepted Answer

a) a2(a-b)-b2(a-c)-c2(b-a)=a2(a-b)-b2(a-c)+c2(a-b)=(a-b)(a2-c2)-b2(a-c)=(a-b)(a-c)(a+c)-b2(a-c)=(a-c)[(a-b)(a+c)-b2]b)a(b-c)3+b(c-a)3+c(a-b)3=a(b-c)3-b[(a-b)+(b-c)]+c(a-b)3=a(b-c)3-b[(a-b)3+3(a-b)2(b-c)+3(a-b)(b-c)2+(b-c)3]+c(a-b)3=a(b-c)3-b(a-b)3+3b(a-b)2(b-c)+3b(a-b)(b-c)2+b(b-c)3+c(a-b)3=(b-c)3(a-b)-(a-b)3(b-c)-3b(a-b)(b-c)(a-b+b-c)=(b-c)3(a-b)-(a-b)3(b-c)-3b(a-b)(b-c)(a-c)=(a-b)(b-c)[(b-c)2-(a-b)2-3b(a-c)]=(a-b)(b-c)[(b-c-a+b)(b-c+a-b)-3b(a-c)]=(a-b)(b-c)[(2b-a-c)(a-c)-3b(a-c)]=(a-b)(b-c)(a-c)(2b-a-c-3b)=-(a-b)(b-c)(a-c)(a+b+c)=(a-b)(b-c)(c-a)(a+b+c)c)abc-(ab+ac+bc)+(a+b+c)-1=abc-ab-ac-bc+a+b+c-1=abc-bc-ab+b-ac+c+a-1=bc(a-1)-b(a-1)-c(a-1)+a-1=(a-1)(bc-b-c+1)=(a-1)[b(c-1)-(c-1)]=(a-1)(c-1)(b-1)=(a-1)(b-1)(c-1)Câu trả lời: a) a2(a-b)-b2(a-c)-c2(b-a)=a2(a-b)-b2(a-c)+c2(a-b)=(a-b)(a2-c2)-b2(a-c)=(a-b)(a-c)(a+c)-b2(a-c)=(a-c)[(a-b)(a+c)-b2]b)a(b-c)3+b(c-a)3+c(a-b)3=a(b-c)3-b[(a-b)+(b-c)]+c(a-b)3=a(b-c)3-b[(a-b)3+3(a-b)2(b-c)+3(a-b)(b-c)2+(b-c)3]+c(a-b)3=a(b-c)3-b(a-b)3+3b(a-b)2(b-c)+3b(a-b)(b-c)2+b(b-c)3+c(a-b)3=(b-c)3(a-b)-(a-b)3(b-c)-3b(a-b)(b-c)(a-b+b-c)=(b-c)3(a-b)-(a-b)3(b-c)-3b(a-b)(b-c)(a-c)=(a-b)(b-c)[(b-c)2-(a-b)2-3b(a-c)]=(a-b)(b-c)[(b-c-a+b)(b-c+a-b)-3b(a-c)]=(a-b)(b-c)[(2b-a-c)(a-c)-3b(a-c)]=(a-b)(b-c)(a-c)(2b-a-c-3b)=-(a-b)(b-c)(a-c)(a+b+c)=(a-b)(b-c)(c-a)(a+b+c)c)abc-(ab+ac+bc)+(a+b+c)-1=abc-ab-ac-bc+a+b+c-1=abc-bc-ab+b-ac+c+a-1=bc(a-1)-b(a-1)-c(a-1)+a-1=(a-1)(bc-b-c+1)=(a-1)[b(c-1)-(c-1)]=(a-1)(c-1)(b-1)=(a-1)(b-1)(c-1)

Khoá học trên OLM (olm.vn)

Khoá học trên OLM (olm.vn)