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多项式x2y-y2z+z2x-x2z+y2x+z2y-2xyz因式分解后的结果是()A.(y-z)(x+y)(x-z)B.(y-z)(x-y)(x+z)C.(y+z)(x-y)(x+z)D.(y+z)(x+y)(x-z)
题目详情
多项式x2y-y2z+z2x-x2z+y2x+z2y-2xyz因式分解后的结果是( )
A. (y-z)(x+y)(x-z)
B. (y-z)(x-y)(x+z)
C. (y+z)(x-y)(x+z)
D. (y+z)(x+y)(x-z)
A. (y-z)(x+y)(x-z)
B. (y-z)(x-y)(x+z)
C. (y+z)(x-y)(x+z)
D. (y+z)(x+y)(x-z)
▼优质解答
答案和解析
x2y-y2z+z2x-x2z+y2x+z2y-2xyz
=(y-z)x2+(z2+y2-2yz)x+z2y-y2z
=(y-z)x2+(y-z)2x-yz(y-z)
=(y-z)[x2+(y-z)x-yz]
=(y-z)(x+y)(x-z).
故选A.
=(y-z)x2+(z2+y2-2yz)x+z2y-y2z
=(y-z)x2+(y-z)2x-yz(y-z)
=(y-z)[x2+(y-z)x-yz]
=(y-z)(x+y)(x-z).
故选A.
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