已知-3x^m-2ny^3与1\5x^5y^n+m是同类项,求(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)的值
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![已知-3x^m-2ny^3与1\5x^5y^n+m是同类项,求(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)的值](/uploads/image/z/1611597-21-7.jpg?t=%E5%B7%B2%E7%9F%A5-3x%5Em-2ny%5E3%E4%B8%8E1%5C5x%5E5y%5En%2Bm%E6%98%AF%E5%90%8C%E7%B1%BB%E9%A1%B9%2C%E6%B1%82%28m-2n%29%5E2-5%28m%2Bn%29-2%28m-2n%29%5E2%2B%28m%2Bn%29%E7%9A%84%E5%80%BC)
已知-3x^m-2ny^3与1\5x^5y^n+m是同类项,求(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)的值
已知-3x^m-2ny^3与1\5x^5y^n+m是同类项,求(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)的值
已知-3x^m-2ny^3与1\5x^5y^n+m是同类项,求(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)的值
因为-3x^m-2ny³与1\5x^5y^n+m是同类项,所以两个代数式中相同字母的指数相等
所以有:
m-2n=5且n+m=3
(m-2n)²-5(m+n)-2(m-2n)²+(m+n)
=[(m-2n)²-2(m-2n)²]+[-5(m+n)+(m+n)]
=-(m-2n)²-4(m+n)
=-5²-4×3
=-25-12
= -37
∵-3x^m-2ny^3与1\5x^5y^n+m是同类项
∴m-2n=5
n+m=3
(m-2n)^2-5(m+n)-2(m-2n)^2+(m+n)
=-(m-2n)^2-4(m+n)
=-5^2-4*3
=-25-12
=-37