Câu hỏi của Lee Min Ho

Question

Phân tích các đa thức sau thành nhân tử:a) x(y2-z2)+y(z2-x2)+z(x2-y2)b) x(y+z)2+y(z+x)2+z(x+y)2-4xyz

Moon Light · Accepted Answer

b)x(y+z)2+y(z+x)2+z(x+y)2-4xyz=[x(y+z)2-2xyz]+[y(z+x)2-2xyz]+z(x+y)2=x(y2+2yz+z2-2yz)+y(x2+z2+2xz-2xz)+z(x+y)2=x(y2+z2)+y(x2+z2)+z(x+y)2=xy2+xz2+x2y+yz2+(xz+yz)(x+y)=xy(x+y)+z2(x+y)+(xz+yz)(x+y)=(x+y)(xy+z2+xz+yz)=(x+y)[x(y+z)+z(y+z)]=(x+y)(y+z)(x+z)Câu trả lời: b)x(y+z)2+y(z+x)2+z(x+y)2-4xyz=[x(y+z)2-2xyz]+[y(z+x)2-2xyz]+z(x+y)2=x(y2+2yz+z2-2yz)+y(x2+z2+2xz-2xz)+z(x+y)2=x(y2+z2)+y(x2+z2)+z(x+y)2=xy2+xz2+x2y+yz2+(xz+yz)(x+y)=xy(x+y)+z2(x+y)+(xz+yz)(x+y)=(x+y)(xy+z2+xz+yz)=(x+y)[x(y+z)+z(y+z)]=(x+y)(y+z)(x+z)

Moon Light · Answer

a)x(y2-z2)+y(z2-x2)+z(x2-y2)=x(y-z)(y+z)+yz2-x2y+x2z-y2z=(y-z)(xy+xz)-x2(y-z)-yz(y-z)=(y-z)(xy+xz-x2-yz)=(y-z)[x(y-x)-z(y-x)]=(y-z)(y-x)(x-z)Câu trả lời: a)x(y2-z2)+y(z2-x2)+z(x2-y2)=x(y-z)(y+z)+yz2-x2y+x2z-y2z=(y-z)(xy+xz)-x2(y-z)-yz(y-z)=(y-z)(xy+xz-x2-yz)=(y-z)[x(y-x)-z(y-x)]=(y-z)(y-x)(x-z)

Pham An Duong · Answer

TestCâu trả lời: Test

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