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åå¼=ï¼x-1ï¼(x+1)(x²+1)(x⁴+1)(x^8+1)/(x-1)
=(x²-1)(x²+1)(x⁴+1ï¹ï¹x^8ï¼1ï¹/ï¹x-1ï¹
=ï¹x⁴-1ï¹ï¹x⁴+1ï¹ï¹x^8+1ï¹/ï¹x-1ï¹
=ï¹x^8-1)(x^8+1)/(x-1)
=ï¹x^16-1)/(x-1)
åå¼=ï¼x-1ï¼(x+1)(x²+1)(x⁴+1)(x^8+1)/(x-1)
=(x²-1)(x²+1)(x⁴+1ï¹ï¹x^8ï¼1ï¹/ï¹x-1ï¹
=ï¹x⁴-1ï¹ï¹x⁴+1ï¹ï¹x^8+1ï¹/ï¹x-1ï¹
=ï¹x^8-1)(x^8+1)/(x-1)
=ï¹x^16-1)/(x-1)
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第1个回答 2012-08-23
化解以后分子上是X^16-1 注：X^16的意思是X的16次方
有这么一个公式X^n-1=(X-1)(X^n-1+X^n-2+...+1)
所以X^16-1=(X-1)(X^15+X^14+...+1)
和分母约分以后得到多项式为X^15+X^14+...+1
有这么一个公式X^n-1=(X-1)(X^n-1+X^n-2+...+1)
所以X^16-1=(X-1)(X^15+X^14+...+1)
和分母约分以后得到多项式为X^15+X^14+...+1
第2个回答 2012-08-23
原式=（x-1)/(x-1)*(x+1)(x^2+1)...=(x-1)(x+1)(x^2+1)...(x^5+1)/(x-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)/(x-1)=(x^4-1)(x^4+1)(x^8+1)/(x-1)=(x^8-1)(x^8+1)/(x-1)
=(x^16-1)/(x-1)
=(x^2-1)(x^2+1)(x^4+1)(x^8+1)/(x-1)=(x^4-1)(x^4+1)(x^8+1)/(x-1)=(x^8-1)(x^8+1)/(x-1)
=(x^16-1)/(x-1)
第3个回答 2012-08-23
（x^16-1）/(x-1)
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