探索写出a-b的差的四次方的展开式
a-b=a-b(a-b)^2=a^2-2ab+b^2
(a-b)^3=a^3-3a^2b+3ab^2-b^3
（a-b）^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4
1 -1
1 -2 1
1 -3 3 -1
1 -4 6 -4 1
绛旓細锛a-b锛^4=a^4-4a^3b+6a^2b^2-4ab^3+b^4 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1
绛旓細=a鐨4娆℃柟+2a²b²+b鐨4娆℃柟-4a³b-4ab³+4a²b²=a鐨4娆℃柟-4a³b-4ab³+6a²b²+b鐨4娆℃柟 涓や釜鏁癮鍜宐鐨勫钩鏂逛箣宸紝 灏辨槸浠栦滑鐨勫钩鏂瑰樊锛屽埄鐢ㄥ钩鏂瑰樊鍏紡鍙互鍒嗚В鍥犲紡銆
绛旓細鎺㈢储鍐欏嚭a-b鐨勫樊鐨勫洓娆℃柟鐨灞曞紑寮 a-b=a-b (a-b)^2=a^2-2ab+b^2 (a-b)^3=a^3-3a^2b+3ab^2-b^3 锛坅-b锛塣4=a^4-4a^3b+6a^2b^2-4ab^3+b^4 1 -1 1 -2 1 1 -3 3 -1 1 -4 6 -4 1 锛坅-b锛塣2鐨勫睍寮寮 a²+b²-2ab (1-x...
绛旓細=a^4-4a^3.b+6a^2.b^2-4ab^3+b^4
绛旓細=锛坅^2+b^2+2ab锛塣2 =a^4+(b^2+2ab)^2+2a^2(b^2+2ab) =a^4+b^4+4a^2b^2+4ab^3+2a^2b^2+4a^3b
绛旓細(a-b)^4 =(a^4)+(b^4)-4(a^3)b-4a(b^3)+6(a^2)(b^2)
绛旓細鍋囪涓鏁颁负a,涓鏁颁负b: a鍑b鐨勫洓娆℃柟锛 a鐨勫洓娆℃柟锛媌鐨勫洓娆℃柟锛6a鐨勫钩鏂逛箻b鐨勫钩鏂癸紞4a鐨勪笁娆℃柟涔榖锛4a涔榖鐨勪笁娆℃柟
绛旓細=[锛圕鍥涘洓锛*a^4]*b^0+[锛圕鍥涗笁锛*a^3]*(-b)^1+ [(C鍥涗簩)*a^2]*(-b)^2+[(C鍥涗竴锛*a^1]*锛-b锛塣3+[(C鍥涢浂锛*a^0]*锛-b锛塣4 =a^4-4(a^3)*b+12(a^2)b^2-4ab^3+b^4
绛旓細锛a锛峛锛鐨4娆℃柟 瑙ｏ細鍘熷紡鈶狅紳锛坅锛峛锛壜凤紙a锛峛锛壜凤紙a锛峛锛壜凤紙a锛峛锛夆憽锛濓紙a²锛峚b锛峚b锛媌²锛壜凤紙a²锛峚b锛峚b锛媌²锛夆憿锛濓紙a²锛2ab锛媌²锛壜凤紙a²锛2ab锛媌²锛夆懀锛濓紙a²锛媌²锛夛紞2ab路锛坅²锛媌²锛夛紞...
绛旓細鍥涙鏂宸叕寮忥細锛a-b)^4=(a^2+b^2)(a+b)(a-b)锛涳紙a-b)^4)=(a+bi)(a-bi)锛坅+b)(a-b)锛岋紙i涓鸿櫄鏁板崟浣嶏級銆傚湪鏁板鐨勫涔犱腑锛屾湁鏃跺欎細纰板埌姹備袱鏁扮殑骞虫柟宸殑棰樼洰銆傞氳繃闈㈢Н鍜屼綋绉殑璁＄畻鍏紡锛屽彲浠ユ帹鍑虹浉閭讳袱鏁颁簩娆℃柟鍜屼笁娆℃柟鐨璁＄畻瑙勫緥锛屽啀灏嗗叾鎺ㄦ紨鍒颁笉鐩搁偦涓や釜鏁扮殑N娆℃柟锛屽悓鏍...
