1-X的立方，能因式分解 X的立方减一，可以怎么因式分解
\u4e00\u51cfX\u7684\u4e09\u6b21\u65b9\u600e\u4e48\u56e0\u5f0f\u5206\u89e31-x^3=(1-x)(1+x+x^2)\u8c22\u8c22\u91c7\u7eb3\uff01
\u53ef\u4ee5\u901a\u8fc7\u6dfb\u9879\uff0c\u518d\u5206\u7ec4\u5206\u89e3
x³-1
=x³-x+x-1
=(x³-x)+(x-1)
=x(x²-1)+\uff08x-1\uff09
=x(x+1)(x-1)+(x-1)
=(x-1)[x(x+1)+1]
=(x-1)(x²+x+1)
=1-x+x-x²+x²-x³
=(1-x)+x(1-x)+x²(1-x)
=(1-x)(1+x+x²)
=（1-x)(1+x+x²)
绛旓細=(1-x)+x(1-x)+x²(1-x)=(1-x)(1+x+x²)
绛旓細1-x^3=(1-x)(1+x+x^2)璋㈣阿閲囩撼锛
绛旓細1鍑x鐨勪笁娆℃柟鍒嗚В鍥犲紡鏄-x³=锛1-x锛夛紙1+x+x²锛=锛1+x+x²锛夈侊紙1-x锛1-x³=1-x+x-x²+x²-x³=(1-x)+x(1-x)+x²(1-x)=(1-x)(1+x+x²)銆傚垎瑙ｅ洜寮忎竴鑸寚鍥犲紡鍒嗚В锛屾妸涓涓椤瑰紡鍦ㄤ竴涓寖鍥达紝濡傚疄鏁拌寖鍥村唴鍒嗚В锛屽嵆鎵...
绛旓細1鍑x鐨3娆℃柟杩欐牱鍥犲紡鍒嗚В 1-x³=锛1-x锛夛紙1+x+x²锛=锛1+x+x²锛夛紙1-x锛1-x³=1-x+x-x²+x²-x³=(1-x)+x(1-x)+x²(1-x)=(1-x)(1+x+x²)
绛旓細(1-x)(1+x+x^2)
绛旓細x鐨勪笁娆℃柟鍑1鍒嗚В鍥犲紡涓(x-1)*(x^2+x+1)銆傝В鍘熷紡x涓夋鏂鍑1锛屾槸涓ら」寮忥紝涓涓槸x鐨勪笁娆℃柟锛鍙︿竴涓槸1涔熷彲浠ョ湅浣1鐨勪笁娆★紝鍙互鐢ㄧ珛鏂瑰樊鍏紡锛屼袱涓暟鐨勭珛鏂瑰樊绛変簬涓ゆ暟鐨勫樊涓(绗竴鏁扮殑骞虫柟鍔犵涓鏁板姞绗簩鏁)鐨勭Н銆傛墍浠ュ師寮忕瓑(x-1)*(x^2+x+1)銆傝В锛歺^3-1=x^3-x^2+x^2-...
绛旓細鍗x^3-1鍙鍥犲紡鍒嗚В涓簒^3-1=(x-1)*(x^2+x+1)銆傚洜寮忓垎瑙ｄ笌瑙ｉ珮娆℃柟绋嬫湁瀵嗗垏鐨勫叧绯伙細瀵逛簬涓鍏冧竴娆℃柟绋嬪拰涓鍏冧簩娆℃柟绋嬶紝鍒濅腑宸叉湁鐩稿鍥哄畾鍜屽鏄撶殑鏂规硶锛屽湪鏁板涓婂彲浠ヨ瘉鏄庯紝瀵逛簬涓鍏冧笁娆℃柟绋嬪拰涓鍏冨洓娆℃柟绋嬶紝涔熸湁鍥哄畾鐨勫叕寮忓彲浠ユ眰瑙ｃ鍒嗚В鍥犲紡鐨勭粨鏋滃繀椤绘槸浠ヤ箻绉殑褰㈠紡琛ㄧず銆傛瘡涓洜寮忓繀椤绘槸鏁村紡锛...
绛旓細x鐨勪笁娆℃柟鍑1鍒嗚В鍥犲紡涓(x-1)*(x^2+x+1)銆傝В锛歺^3-1=x^3-x^2+x^2-x+x-1 =(x^3-x^2)+(x^2-x)+(x-1)=x^2*(x-1)+x*(x-1)+(x-1)=(x-1)*(x^2+x+1)鍗硏^3-1鍙鍥犲紡鍒嗚В涓簒^3-1=(x-1)*(x^2+x+1)銆
绛旓細x^3-1 =x^3-1^3 =(x-1)(x^2+x+1)鏍规嵁绔嬫柟宸叕寮
绛旓細瑕佸洜寮忓垎瑙 x^3 - 1锛鎴戜滑鍙互浣跨敤绔嬫柟宸叕寮忥紝瀹冩槸涓涓壒娈鐨勫洜寮忓垎瑙鍏紡銆傜珛鏂瑰樊鍏紡鏄竴涓敤浜庡皢涓や釜绔嬫柟鏁扮浉鍑忕殑鍏紡锛屽舰寮忓涓嬶細a^3 - b^3 = (a - b)(a^2 + ab + b^2)鍦ㄨ繖涓壒娈婄殑渚嬪瓙涓紝鎴戜滑鏈 x^3 - 1锛屽彲浠ュ皢瀹冪湅浣 a^3 - b^3 鐨勫舰寮忥紝鍏朵腑 a = x锛b = 1銆
