(x+y)^2-4(x+y-1)(x^2-4x)^2+8(x^2-4x)+16
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 17:51:00
![(x+y)^2-4(x+y-1)(x^2-4x)^2+8(x^2-4x)+16](/uploads/image/z/5090447-47-7.jpg?t=%28x%2By%29%5E2-4%28x%2By-1%29%28x%5E2-4x%29%5E2%2B8%28x%5E2-4x%29%2B16)
(x+y)^2-4(x+y-1)(x^2-4x)^2+8(x^2-4x)+16
(x+y)^2-4(x+y-1)
(x^2-4x)^2+8(x^2-4x)+16
(x+y)^2-4(x+y-1)(x^2-4x)^2+8(x^2-4x)+16
(x+y)^2-4(x+y-1)=(x+y)^2-4(x+y)+4=(x+y-2)^2
(x^2-4x)^2+8(x^2-4x)+16=(x^2-4x+4)^2
=(x+y)^2-4(x+y)+4=[(x+y)-2}^2=(x+y-2)^2
=(x^2-4x+4)^2=(x-2)^4
1:
原式=(x+y)^2-4(x+y)+4=(x+y-2)^2 把X+Y看成一个数算
2:把x^2-4x看成一个数设为t
原式=t^2+8t+16=(t+4)^2
在把t带回去=(x^2-4x+4)^2=[(x-2)^2]^2=(x-2)^4