如果(x^m/x^2n)^3/x^m-n与4x^2是同类项,且2m+5n=6,求4m^2-25n^2的值

答
(x^m/x^2n)^3/x^(m-n)
=[x^(m-2n)]^3/x^(m-n)
=x^3(m-2n)/x^(m-n)
=x^(3m-6n-m+n)
=x^(2m-5n)
与4x^2是同类项
所以
2m-5n=2
2m+5n=6
解方程组
得
m=2
n=2/5
4m^2-25n^2
=4×4-25×4/25
=16-4
=12