求(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)

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求(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)
求(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)

求(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)
(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)
=(a8+b8)(a4+b4)(a2+b2)(a2-b2)
=(a8+b8)(a4+b4)(a4-b4)
=(a8+b8)(a8-b8)
=a16-b16

其实这道题就是连续使用4次平方差公式，
(a^+b^8)(a^4+b^4)(a^2+b^2)(a+b)(a-b)=(a^+b^8)(a^4+b^4)(a^2+b^2)(a^2-b^2)
=(a^+b^8)(a^4+b^4)(a^4-b^4)
...

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其实这道题就是连续使用4次平方差公式，
(a^+b^8)(a^4+b^4)(a^2+b^2)(a+b)(a-b)=(a^+b^8)(a^4+b^4)(a^2+b^2)(a^2-b^2)
=(a^+b^8)(a^4+b^4)(a^4-b^4)
=(a^+b^8)(a^8-b^8)
=a^16-b^16

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(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b)
=(a8+b8)(a4+b4)(a2+b2)(a2-b2)
=(a8+b8)(a4+b4)(a4-b4)
=(a8+b8)(a8-b8)
=a16-b16

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