若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项,且2m+5n=6,求4m^2-25n^2

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若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项,且2m+5n=6,求4m^2-25n^2

若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项,且2m+5n=6,求4m^2-25n^2
若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项,且2m+5n=6,求4m^2-25n^2

若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项,且2m+5n=6,求4m^2-25n^2
(x^m÷x^2n)^3÷x^(m-n)=(x^(m-2n))^3÷x^(m-n)=x^(3m-6n-m+n)=x^(2m-5n)
∵(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项
∴x^(2m-5n)与x^2同类项
∴2m-5n=2
所以4m^2-25n^2=(2m+5n)(2m-5n)=12

(x^m÷x^2n)^3÷x^(m-n)
=x^(3m-6n-m+n)
=x^(2m-5n)
2m-5n=2
2m+5n=6
4m^2-25n^2=(2m-5n)(2m+5n)=2×6=12

若(x^m÷x^2n)^3÷x^(m-n)与x^2为同类项
则 (m - 2n )* 3 -(m-n)=2 是吧
即:2m-5n =2
又2m + 5n = 6
得到:m =2 , n= 2/5

4m^2-25n^2 = 16+4= 20