已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+x(xy+y)的值

题目

已知x+y=-1,xy=-2,求代数式-5（x+y)+(x-y)+x(xy+y)的值

答案

答：
x+y=-1,xy=-2
-5（x+y)+(x-y)+x(xy+y)
=-5x-5y+x-y+xy(x+1)
=-4x-6y+(-2)(x+1)
=-4x-6y-2x-2
=-6x-6y-2
=-6(x+y)-2
=-6×(-1)-2
=6-2
=4