已知m+n=3,mn=-2,求多项式2(mn+m)-[-(3n-mn)-m]+mn的值(先化简,再求值)

问题描述:

已知m+n=3,mn=-2,求多项式2(mn+m)-[-(3n-mn)-m]+mn的值(先化简,再求值)

2(mn + m) - [ -(3n - mn) - m] + mn
= 2mn + 2m + 3n - mn + m + mn
= 2mn + 3m + 3n
= 2mn + 3(m + n)
= 2×(-2) + 3×3
= -4 + 9
= 5

2(mn+m)-[-(3n-mn)-m]+mn
=2(mn+m)-(-3n+mn-m)+mn
=2mn+2m+3n-mn+m+mn
=2mn+3m+3n
=2mn+3(m+n)=5

2mn+2m-(-3n+mn-m)+mn=2mn+3m+3n=2*2+3*(m+n)=4+3*(-2)=-2

原式=2mn+2m+3n-mn+m+mn
=2mn+3(m+n)
=2*(-2)+3*3
=9-4
=5

2(mn+m)-[-(3n-mn)-m]+mn
  =2mn+2m+3n-mn+m+mn
  =2mn+3m+2n
  =2mn+3(m+n)
  ∵m+n=3,mn=-2
  ∴2(mn+m)-[-(3n-mn)-m]+mn
  =2mn+3(m+n)
  =2×(-2)+3×3
  =-4+9
  =5

2(mn+m)-[-(3n-mn)-m]+mn=2mn+2m+3n-mn+m+mn=2mn+3m+3n=-4+9=-5