[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]等于多少

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 14:24:40
[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]等于多少

[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]等于多少
[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]等于多少

[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]等于多少
=(x-y)^2(x+y)^2-2(x-y)(x+y)=(x^2-y^2)^2-2(x^2-y^2)=x^4-2x^2y^2+y^4-2x^2+2y^2

[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]
=(x-y)²(x+y)²-2(x-y)(x+y)
=(x²-y²)(x²-y²-2)

[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]
=3(x-y)^3(x+y)^4[(x-y)(x+y)-2]÷[3﹙x-y﹚²﹙x+y﹚³]
=(x-y)(x+y)(x^2-y^2-2)

[3﹙x-y﹚^4 ﹙x+y﹚^5 -6﹙x-y﹚^3 ﹙x+y﹚^4 ]÷[3﹙x-y﹚²﹙x+y﹚³]
=(x-y)²(x+y)²-2(x-y)(x+y)
=(x²-y²)²-2(x²-y²)
=(x²-y²)(x²-y²-2)