Question

若3x^(m+1)y和6x^(n-1)y^(n-3)是同类项，则m(2n^2-m)+n(2m^2-n)+(m-n)^2=( )?

Answer 1

同类项，意味着幂相等。
即 m+1=n-1
n-3=1
可以求出：n=4，m=2
m(2n^2-m)+n(2m^2-n)+(m-n)^2
=2*(2*4^2-2)+4*(2*2^2-4)+(2-4)^2
=60+16+4
=80

Answer 2

若3x^(m+1)y和6x^(n-1)y^(n-3)是同类项，则m(2n^2-m)+n(2m^2-n)+(m-n)^2=( )?

{ m+1=n-1, n-3=1.
{ m=2, n=4.
m(2n^2-m)+n(2m^2-n)+(m-n)^2
=2×30+4×4+4
=60+16+4
=80.