x的10次方-1因式分解

Question

如题，但答案不是x的5次方+1乘-1！！！

Answer 1

x的10次方-1
=（x的5次方+1）（x的5次方-1）
=（x+1）（x-1）（x的4次方+x的3次方+x²+x+1） （x的4次方-x的3次方+x²-x+1）

Answer 2

(x^10-1=(x-1)(x^9+x^8+...+x+1)=(x-1)(x+1)(x^8+x^6+x^4+x^2+1)

Answer 3

=(x^5+1)(x^5-1)
=(x^5+x^4-x^4-x^3+x^3+x^2-x^2+1)[(x^5-x3)+(x^3-1)]
=[x^4(x+1)-x^3(x-1)+x^2(x+1)-(x-1)(x+1)][x^3(x+1)(x-1) + (x-1)(x^2+x+1)]
=(x+1)(x^4-x^3+x^2-x+1)(x-1)(x^4+x^3+x^2+x+1)

Answer 4

x^10-1
=(x^5)²-1
=(x^5+1)(x^5-1)
=(x+1)(x^4-x³+x²-x+1)(x-1)(x^4+x³+x²+x+1)

Answer 5

x^10-1
=(x^5)²-1
=(x^5+1)(x^5-1)本回答被网友采纳