问题 解答题
把下列各式分解因式:
(1)x3y-xy3
(2)(x2+1)2-4x2
(3)先化简再求值,
x-y
x
÷(x-
2xy-y2
x
)
.其中x=2009,y=2010.
答案

(1)原式=xy(x2-y2

=xy(x+y)(x-y);

(2)原式=(x2+1-2x)(x2+1+2x)

=(x-1)2(x+1)2

(3)原式=

x-y
x
÷
(x-y)2
x

=

x-y
x
×
x
(x-y)2

=

1
x-y

当x=2009,y=2010时,原式=

1
2009-2010
=-1.

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