已知m-n=4,mn=-1,求:(-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值.

问题描述:

已知m-n=4,mn=-1,求:(-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值.

(-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)
=-2mn+2m+3n-3mn-2n+2m-m-4n-mn
=-6mn+3m-3n
=-6mn+3(m-n),
又因为m-n=4,mn=-1,
所以-6mn+3(m-n)=(-6)×(-1)+3×4=6+12=18.
答案解析:先把要求的式子去括号,然后再合并同类项,最后把m-n=4,mn=-1代入式子即可求值.
考试点:整式的加减—化简求值.
知识点:解决本题的关键是把代数式先化简,然后再求值,化简时一定要细心.