Question

先化简，再求值：4x²y-【6xy-2（4xy-2）-xy²】+1.其中x=-二分之一，y=2.（要过程）

Answer 1

4x²y-[6xy-2(4xy-2)-xy²]+1
=4x²y-(6xy-8xy+4-xy²)+1
=4x²y-6xy+8xy-4+xy²+1
=4x²y+2xy+xy²+1
=xy(4x+2+y)+1
=(-2)×2×[4×(-2分之1)+2+2]+1
=-4×2+1
=-7

追问

可以把化简的式子和求值的式子分开再算一遍吗，谢谢

追答

4x²y-[6xy-2(4xy-2)-xy²]+1
=4x²y-(6xy-8xy+4-xy²)+1
=4x²y-6xy+8xy-4+xy²+1
=4x²y+2xy+xy²+1
=xy(4x+2+y)+1

把x=-2分之1，y=2带入式子得：
=(-2分之1)×2×[4×(-2分之1)+2+2]+1
=-1×2+1
=-2

居然看错了！

Answer 2

4x²y-【6xy-2（4xy-2）-xy²】+1
=4x²y-6xy+2（4xy-2）+xy²+1
=4x²y-6xy+8xy-4+xy²+1
=4x²y+2xy+xy²-3
=xy(4x+2+y)-3
当x=-1/2，y=2时
原式=-1×(-2+2+2)-3
=-2-3
=-5