已知X+Y=2.求(x方-y方)的平方-8乘(x方+y方)的值?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 01:01:23

已知X+Y=2.求(x方-y方)的平方-8乘(x方+y方)的值?

已知x+y=2,则:
(x²-y²)² -8(x²+y²)
=[(x+y)(x-y)]²-8(x²+y²)
=4(x-y)²-8(x²+y²)
=4(x²-2xy+y²-2x²-2y²)
=4(-x²-2xy-y²)
=-4(x²+2xy+y²)
=-4(x+y)²
=-4×4
=-16

-16