Question

化简求值:(x-y)的平方+(x+y)(y-x)-2x(1-y),期中x=1,y=-2

Answer 1

(x-y)²+(x+y)(y-x)-2x(1-y)
=(x²-2xy+y²)+(y²-2x²)-(2x-2xy)
=x²-2xy+y²+y²-2x²-2x+2xy
=-x²+2y²-2x
=-1²+2×(-2)²-2×1
=-1+8-2
=5

追问

(x+y)(y-x)=(y²-2x²) 对吗？

追答

明显不对啊

(x-y)²+(x+y)(y-x)-2x(1-y)
=(x²-2xy+y²)+(y²-x²)-(2x-2xy)
=x²-2xy+y²+y²-x²-2x+2xy
=2y²-2x
=2×(-2)²-2×1
=8-2
=6