作业帮(x+y)^2(x-y)^2(x^4+x^2y^2+y^4)^2
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/10/03 02:57:58
(x+y)^2(x-y)^2(x^4+x^2y^2+y^4)^2
30分钟内回答please ,thankyou
30分钟内回答please ,thankyou
(x+y)^2(x-y)^2(x^4+x^2y^2+y^4)
= { (x+y) (x-y) }^2 (x^4+x^2y^2+y^4)
= ( x^2-y^2 )^2 (x^4+x^2y^2+y^4)
= ( x^2-y^2 ) { ( x^2-y^2 ) (x^4+x^2y^2+y^4) }
= ( x^2-y^2 ) { ( x^2)^3 - (y^2) ^3 }
= ( x^2-y^2 ) ( x^6-y^6 )
= x^(2+6) - x^6y^2 - x^2y^6 + y^(2+6)
= x^8 - x^6y^2 - x^2y^6 + y^8
= { (x+y) (x-y) }^2 (x^4+x^2y^2+y^4)
= ( x^2-y^2 )^2 (x^4+x^2y^2+y^4)
= ( x^2-y^2 ) { ( x^2-y^2 ) (x^4+x^2y^2+y^4) }
= ( x^2-y^2 ) { ( x^2)^3 - (y^2) ^3 }
= ( x^2-y^2 ) ( x^6-y^6 )
= x^(2+6) - x^6y^2 - x^2y^6 + y^(2+6)
= x^8 - x^6y^2 - x^2y^6 + y^8
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