(1)(x-y)^2-(2x+y)(y-2x) (2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/27 23:11:32
(1)(x-y)^2-(2x+y)(y-2x) (2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4

(1)(x-y)^2-(2x+y)(y-2x) (2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4
(1)(x-y)^2-(2x+y)(y-2x) (2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4

(1)(x-y)^2-(2x+y)(y-2x) (2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4
(1)(x-y)^2-(2x+y)(y-2x)
=(x²-2xy+y²)-(y²-4x²)
=x²-2xy+y²-y²+4x²
=5x²-2xy
(2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4
x^4-2x^2 y^2+y^4=(x²-y²)²=(x+y)²(x-y)²=(x+y)²(y-x)²=(x+y)(y-x)[(y+x)(y-x)]=(x+y)(y-x)(y²-x²)
∴填y²-x²

第一题的问题是什么

(1)(x-y)^2-(2x+y)(y-2x)
=xx-2xy+yy+4xx-yy
=5xx-2xy
(2)(x+y)(y-x)( )=x^4-2x^2 y^2+y^4
(yy-xx)( )=(xx-yy)^2
(yy-xx)( )=(yy-xx)^2
(yy-xx)( yy-xx)=(yy-xx)^2

(1)(x-y)^2-(2x+y)(y-2x)=x^2-2xy+y^2-(2xy-4x^2+y^2-2xy)=x^2-2xy+y^2+4x^2-y^2=5x^2- 2xy
(2)右侧x^4-2x^2 y^2+y^4=(x^2-y^2)^2 , 左侧(x+y)(y-x)=-(x+y)(x-y)=-(x^2-y^2) ,所以()里为-(x^2-y^2)

(1)(x-y)²-(2x+y)(y-2x)
=(x-y)²-(y²-4x²)
=5x²-2xy
(2)x^4-2x^2 y^2+y^4÷(x+y)(y-x)
=x^4-2x^2 y^2+y^4÷(y²-x²)
=(x+y)²÷(y²-x²)