计算 (x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)

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计算(x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)计算(x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)计算(x^8+y^8)(x^4+y^4)(x

计算 (x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)
计算 (x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)

计算 (x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)
(x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)
=(x^8+y^8)(x^4+y^4)(x^2+y^2)(x^2-y^2)
=(x^8+y^8)(x^4+y^4)(x^4-y^4)
=(x^8+y^8)(x^8-y^8)
=x^16-y^16

x^16-y^16

从后往前算..

先做后两项
(x+y)(x-y)=x^2-y^2
依次向前做
最后得x^16-y^16

从后往前算!
(x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)
=(x^8+y^8)(x^4+y^4)(x^2+y^2)(x^2-y^2)
=(x^8+y^8)(x^4+y^4)(x^4-y^4)
=(x^8+y^8)(x^8-y^8)
=x^16-y^16