(x-y)(_____)=x五次方-y五次方

如题 解答详细点
2025-01-19 22:10:02
推荐回答(1个)
回答1:

x^5-y^5=(x-y)(x^4)+(x^4*y-y^5) 为了方便我先因式分解(x^4*y-y^5),(x^4*y-y^5)=y(x^4-y^4)=y(x^2-y^2)(x^2+y^2)=y(x+y)(x-y)(x^2+y^2) 所以(x-y)(x^4)+(x^4*y-y^5)=(x-y)(x^4)+y(x+y)(x-y)(x^2+y^2)=(x-y)[x^4+y(x+y)(x^2+y^2)]=(x-y)(x^4+y^4+yx^3+xy^3+x^2*y^2) 注:*是符号乘以