问题 选择题

若(x+y)3-xy(x+y)=(x+y)•A,则A为(  )

A.x2+y2

B.x2-xy+y2

C.x2-3xy+y2

D.x2+xy+y2

答案

∵(x+y)3-xy(x+y),

=(x+y)[(x+y)2-xy],

=(x+y)(x2+xy+y2),

又∵(x+y)3-xy(x+y)=(x+y)•A,

∴A=x2+xy+y2

故选D.

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