计算题14、（12分）计算:[x(x2y2-xy)-y(x2-x3y)]÷x2y15、（1814、（12分）计算:[x(x2y2-xy)-y(x2-x3y)]÷x2y15、（18分）已知m2=n+2，n2=m+2(m≠n),求m3-2mn+n3

Question

计算题 14、（12分） 计算:[x(x2y2-xy)-y(x2-x3y)]÷x2y 15、（18
14、（12分）
计算:[x(x2y2-xy)-y(x2-x3y)]÷x2y
15、（18分）已知m2=n+2，n2=m+2(m≠n),求m3-2mn+n3

Answer 1

[x(x2y2-xy)-y(x2-x3y)]÷x2y
=[x2y(xy-1)+x2y(xy-1)]÷x2y
=2x2y(xy-1)/x2y
=2(xy-1)
=2xy-2
m2=n+2,n2=m+2
m2-n2=-(m-n)
(m-n)(m+n+1)=0
m≠n,m+n+1=0
,m+n= -1
m2+n2+2mn=1,m2+n2=m+2+n+2=3
mn= -1
m3-2mn+n3=(m+n)(m2-mn+n2)-2mn
=(m+n)(n+2-mn+m+2)-2mn
= -(3-mn)-2mn=-3-mn= -3+1= -2