推 peter015 : 感謝 08/20 00:01
※ 引述《peter015 (hi)》之銘言：
: (1+x+x^2+x^3+x^4+x^5)^2015乘(1-x+x^2-x^3+x^4-x^5)^2015
: 展開式中X的253次方項的係數為何?
: 謝謝~
先化簡原多項式:
原式 = {(1+x+x^2+x^3+x^4+x^5)(1-x+x^2-x^3+x^4-x^5)}^2015
= {[(1+x^2+x^4)+(x+x^3+x^5)][(1+x^2+x^4)-(x+x^3+x^5)]}^2015
= {(1+x^2+x^4)^2 - (x+x^3+x^5)^2}^2015
= {(1+x^2+x^4)^2 - x^2 * (1+x^2+x^4)^2}^2015
= {(1-x^2)(1+x^2+x^4)^2}^2015
到這裡應該可以明顯地看出來原式只有偶次方項, 故所求為 0 #
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