填空(x-y)(x2+xy+y2)=______;(x-y)(x3+x2y+xy2+y3)=______根据以上等式进行猜想,当n是偶数时,可得:(x-y)(x
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填空(x-y)(x2+xy+y2)=______;(x-y)(x3+x2y+xy2+y3)=______ 根据以上等式进行猜想,当n是偶数时,可得:(x-y)(xn+xn-1y+yn-2y2+…+x2yn-2+xyn-1+yn)=______. |
答案
原式=x3+x2y+xy2-x2y-xy2-y3=x3-y3; 故答案为:x3-y3; 原式=x4+x3y+x2y2+xy3-x3y-x2y2-xy3-y4=x4-y4; 故答案为:x4-y4; 原式=xn+1+xny+xyn-2+x2yn-1+xyn-xny-xn-1y2-yn-1y2-…-x2yn-1-xyn-yn+1=xn+1-yn+1, 故答案为:xn+1-yn+1. |
举一反三
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