Câu hỏi của Võ Minh Tiến

Question

Phân tích đa thức thành nhân tử:a) x3+y3+z3-3xyzb)a2(b-c)+b2(c-a)+c2(a-b)

Minh Triều · Accepted Answer

a) x3+y3+z3-3xyz=(x+y)3+z3-3x2y-3xy2-3xyz=(x+y+z).[(x+y)2+(x+y).z+z2]-3xy.(x+y+z)=(x+y+z)(x2+2xy+y2+zx+zy+z2)-3xy.(x+y+z)=(x+y+z)(x2+2xy+y2+zx+zy+z2-3xy)=(x+y+z)(x2+y2+zx+zy+z2-zy) b)a2(b-c)+b2(c-a)+c2(a-b)=a2b-a2c+b2c-b2a+c2a-c2b=(a2b-c2b)+(-a2c+c2a)+(b2c-b2a)=b.(a2-c2)-ac.(a-c)-b2.(a-c)=b.(a+c)(a-c)-ac.(a-c)-b2.(a-c)=(a-c)[b.(a+c)-ac-b2]=(a-c)(ab+bc-ac-b2)=(a-c)[(ab-ac)+(bc-b2)]=(a-c)[a.(b-c)-b.(b-c)]=(a-c)(b-c)(a-b)Câu trả lời:  a) x3+y3+z3-3xyz=(x+y)3+z3-3x2y-3xy2-3xyz=(x+y+z).[(x+y)2+(x+y).z+z2]-3xy.(x+y+z)=(x+y+z)(x2+2xy+y2+zx+zy+z2)-3xy.(x+y+z)=(x+y+z)(x2+2xy+y2+zx+zy+z2-3xy)=(x+y+z)(x2+y2+zx+zy+z2-zy) b)a2(b-c)+b2(c-a)+c2(a-b)=a2b-a2c+b2c-b2a+c2a-c2b=(a2b-c2b)+(-a2c+c2a)+(b2c-b2a)=b.(a2-c2)-ac.(a-c)-b2.(a-c)=b.(a+c)(a-c)-ac.(a-c)-b2.(a-c)=(a-c)[b.(a+c)-ac-b2]=(a-c)(ab+bc-ac-b2)=(a-c)[(ab-ac)+(bc-b2)]=(a-c)[a.(b-c)-b.(b-c)]=(a-c)(b-c)(a-b)

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