(x+1)的平方可以用完全平方公式，那么三次方，四次方呢，有没有什么公示之类的呢？请告诉我。 (x+1)平方怎么算
\u5173\u4e8e\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7684\u6570\u5b66\u9898\u89e3:a^2+1/a^2=(a+1/a)^2-2=16-2=14.
\u5206\u6790:\u9047\u5230\u6b64\u7c7b\u9898\u76ee,\u6211\u4eec\u9996\u5148\u8981\u60f3\u7684\u662f\u95ee\u9898\u4e0e\u5df2\u77e5\u6761\u4ef6\u4e4b\u95f4\u7684\u6570\u5b57\u7684\u8054\u7cfb.
\u5728\u672c\u9898\u4e2d\u5df2\u77e5a+1/a=4 ,\u800c\u95ee\u9898\u662fa^2+1/a^2 ,\u7531\u6b64\u6211\u4eec\u5c31\u53ef\u4ee5\u53bb\u60f3\u5230\u5148\u53bb\u51d1\u4e00\u4e2a(a+1/a)^2\u7b49\u4e8e\u51e0\uff0c\u663e\u7136\u662f16\uff1b
\u800c\u8981\u6c42\u7684\u662fa^2+1/a^2\uff0c\u90a3\u4e48\u6211\u4eec\u770b\u5230\u201c\uff08a+1/a)^2\u201c\u662f\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5c55\u5f00\u6765\u5c31\u662fa^2+2+1/a^2\uff0c\u4e0e\u8981\u6c42\u7684a^2+1/a^2\u5c31\u5dee\u4e00\u4e2a2\uff0c\u6240\u4ee5\u51cf\u53bb2\u5c31\u662f\u95ee\u9898\u7684\u7b54\u6848\u4e86\u3002
\u6240\u4ee5\u505a\u6b64\u7c7b\u95ee\u9898\u7684\u65b9\u6cd5\u662f\uff1a\uff081\uff09\u89c2\u5bdf\u5df2\u77e5\u6761\u4ef6\u4e0e\u95ee\u9898\u7684\u6570\u5b57\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u662f\u5426\u53ef\u4ee5\u51d1\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u7b49\uff09\uff0c\uff082\uff09\u51d1\u597d\u516c\u5f0f\u4e4b\u540e\u628a\u5df2\u77e5\u6761\u4ef6\u4ee3\u5165\u8fdb\u53bb\uff1b\uff083\uff09\u628a\u51d1\u597d\u7684\u516c\u5f0f\u4e0e\u8981\u6c42\u7684\u95ee\u9898\u7684\u6570\u5b57\u518d\u505a\u5bf9\u6bd4\uff0c\u628a\u5dee\u5f02\u90e8\u5206\u627e\u51fa\u6765\uff1b\uff084\uff09\u5199\u7b54\u6848\u3002
(x+1)\u5e73\u65b9\u7684\u89e3\u7b54\u8fc7\u7a0b\u5982\u4e0b\uff1a
\uff08x+1\uff09²
=\uff08x+1\uff09\uff08x+1\uff09\uff08\u8fd9\u91cc\u662f\u628a\uff08x+1\uff09²\u62c6\u5f00\uff09
=x²+x+x+1\uff08\u8fd9\u91cc\u662f\u7b2c\u4e00\u9879\u91cc\u7684x+1\u5206\u522b\u76f8\u4e58\u7b2c\u4e8c\u9879\u7684x+1\uff09
\uff1dx²+2x+1
\u6269\u5c55\u8d44\u6599\uff1a
\u4e24\u6570\u548c\u7684\u5e73\u65b9\uff0c\u7b49\u4e8e\u5b83\u4eec\u7684\u5e73\u65b9\u548c\u52a0\u4e0a\u5b83\u4eec\u7684\u79ef\u76842\u500d\u3002
\uff08a+b\uff09²=a²+2ab+b²
\u4e24\u6570\u5dee\u7684\u5e73\u65b9\uff0c\u7b49\u4e8e\u5b83\u4eec\u7684\u5e73\u65b9\u548c\u51cf\u53bb\u5b83\u4eec\u7684\u79ef\u76842\u500d\u3002
\ufe59a\uff0db\ufe5a²=a²\ufe632ab+b²
\u4e09\u4e2a\u6570\u7684\u548c\u7684\u5e73\u65b9\uff1a
\uff08a+b+c\uff09²
=\uff08a+b+c\uff09\u00b7\uff08a+b+c\uff09
=a²+ab+ac+b²+ab+bc+c²+ac+bc
=a²+b²+c²+2ab+2ac+2bc
\u53c2\u8003\u8d44\u6599\uff1a\u767e\u5ea6\u767e\u79d1-\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f
(x+1)³=x³+3x²+3x+1
(x+1)^4=x^4+4x³+6x²+4x+1
......^5=1...+5...+10...+10...+5...+1
......^6=1...+6...+15...+20...+15...+6...+1
......^7=1...+7...+21...+35...+35...+21...+7...+1
......
(杨辉三角)
绛旓細X1=-1+鈭421锛孹2=-1-鈭421銆
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绛旓細a-1^2琛ㄧず(a-1)鐨勫钩鏂锛2a(a-1)琛ㄧず涓や釜鏁癮鍜宎-1鐨勪箻绉瀹屽叏骞虫柟鍏紡鏄敱涓変釜閮ㄥ垎缁勬垚鐨勶細绗竴涓儴鍒嗘槸(a-1)^2锛岃〃绀(a-1)鐨勫钩鏂癸紱绗簩涓儴鍒嗘槸2a(a-1)锛岃〃绀轰袱涓暟a鍜宎-1鐨勪箻绉紱绗笁涓儴鍒嗘槸1^2锛岃〃绀1鐨勫钩鏂广傚舰寮忓浐瀹氾細瀹屽叏骞虫柟鍏紡鐨勫舰寮忔槸鍥哄畾鐨勶紝鏃犺a鍙栦綍鍊硷紝鍏紡鐨...
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绛旓細(x+1)²=x²+2x+1 (x+1)³=x³+3x²+3x+1 (x+1)^4=x^4+4x³+6x²+4x+1 ...^5=1...+5...+10...+10...+5...+1 ...^6=1...+6...+15...+20...+15...+6...+1 ...^7=1...+7...+21...+35...+35...+...
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绛旓細1銆佷互涓婂椤瑰紡锛屾寚鐨勯兘鏄疄绯绘暟澶氶」寮忋傛墍浠ヤ笉鑳界ОA= -P^2+2PQ-Q^2涓瀹屽叏骞虫柟寮忥紝鍥犱负涓嶅瓨鍦ㄤ互P銆丵涓哄彉鍏冪殑瀹炵郴鏁板椤瑰紡B锛屼娇A=B^2銆2銆佷互涓婃墍璇村椤瑰紡锛岄兘鏄畝鍗曞彉鍏冪殑澶氶」寮忋備笉鑳介殢渚跨О涓涓唬鏁板紡鎴栦笁瑙掑嚱鏁板紡涓哄畬鍏ㄥ钩鏂瑰紡銆傗憼灏界鏈墄^2-2+1/x^2=(x-1/x)^2锛屼絾鏄洜涓鸿繖閲寈^2-...
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