先化简,再求值:(x-y)(x+y)-(x+y)^2+2y(y-x),其中x=1,y=3.

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/07 17:23:26
先化简,再求值:(x-y)(x+y)-(x+y)^2+2y(y-x),其中x=1,y=3.

先化简,再求值:(x-y)(x+y)-(x+y)^2+2y(y-x),其中x=1,y=3.
先化简,再求值:(x-y)(x+y)-(x+y)^2+2y(y-x),其中x=1,y=3.

先化简,再求值:(x-y)(x+y)-(x+y)^2+2y(y-x),其中x=1,y=3.
原式
=(x-y)(x+y)-(x+y)^2+2y(y-x)
=(x+y)(x-y-x-y)-2y(x-y)
=-2y(x+y)-2y(x-y)
=-2y(x+y+x-y)
=-2y×(-2x)
=4xy
将x=1,y=3代入,有:
原式=4xy=4×1×3=12.

(x-y)(x+y)-(x+y)^2+2y(y-x)
=(x-y)(x+y-2y)-(x+y)^2
=(x-y)^2-(x+y)^2
=(x-y+x+y)(x-y-x-y)
=2x*(-2y)
=-4xy
=-4*1*3=-12