以知单项式M.N满足3X(M+6X^2)=18XY+N,求M和N

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以知单项式M.N满足3X(M+6X^2)=18XY+N,求M和N
以知单项式M.N满足3X(M+6X^2)=18XY+N,求M和N

以知单项式M.N满足3X(M+6X^2)=18XY+N,求M和N
把原式
3x(m+6x²)=18xy+n
脱括号并移项得
18x³+3mx-18xy-n=0
可以发现,要想对所有的x、y都成立,18x³-18xy≠0,所以只可能有两种情况：
情况一：
18x³+3mx=0,且-18xy-n=0
可解得：
m=-6x²
n=-18xy
情况二：
18x³-n=0,且3mx-18xy=0
可解得：
m=6y
n=18x³

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