x^3-1的因式分解是多少 因式分解x的三次方减一为什么等于
1-X^3 \u56e0\u5f0f\u5206\u89e31-X^3=(1-x)(1+x+x^2)
\u5206\u6790\uff1a
\u516c\u5f0fa^3-b^3=(a-b)(a^2+ab+b^2)
\u52191-X^3=(1-x)(1+x+x^2)
\u6269\u5c55\u8d44\u6599
\u5176\u4ed6\u76f8\u5173\u516c\u5f0f\uff1a
\uff081\uff09\uff08a+b\uff09³\uff1da³\uff0b3a²b\uff0b3ab²\uff0bb³
\uff082\uff09a³+b³=a³+a²b-a²b+b³=a²\uff08a+b\uff09-b\uff08a²-b²\uff09=a²\uff08a+b\uff09-b\uff08a+b\uff09\uff08a-b\uff09
=\uff08a+b\uff09[a²-b\uff08a-b\uff09]=\uff08a+b\uff09\uff08a²-ab+b²\uff09
\uff083\uff09a³-b³=a³-a²b+a²b-b³=a²\uff08a-b\uff09+b\uff08a²-b²\uff09=a²\uff08a-b\uff09+b\uff08a+b\uff09\uff08a-b\uff09
=\uff08a-b\uff09[a²+b\uff08a+b\uff09]=\uff08a-b\uff09\uff08a²+ab+b²\uff09
\u56e0\u6570\u5206\u89e3X³-1=(X-1)(X²+X+1)
\u63a8\u7b97\u5982\u4e0b\uff1a
X³-1
=X³-X²+X²-X+X-1
=X²\uff08X-1\uff09+X\uff08X-1\uff09+\uff08X-1\uff09
=\uff08X-1\uff09\uff08X²+X+1\uff09
x³ - 1 =(x - 1)(x² + x + 1)
绛旓細x³-1=(x-1)(x²+x+1)
绛旓細鍗硏^3-1鍙洜寮忓垎瑙ｄ负x^3-1=(x-1)*(x^2+x+1)銆
绛旓細瑙ｏ細x^3-1=(x-1)(x^2+x+1)x^2+x+1=0 1-4x1x1=1-4=-3<0 娌℃湁瀹炴暟瑙ｏ紝鎵浠ヨ繖涓簩娆′笁椤瑰紡涓嶈兘鍒嗚В 绔嬫柟宸叕寮 a^3+-b^3=(a+-b)(a^2-+ab+b^2)
绛旓細鍗硏^3-1鍙洜寮忓垎瑙ｄ负x^3-1=(x-1)*(x^2+x+1)銆傚垎瑙ｅ洜寮忔椂瑕侀伒寰殑鍘熷垯鏈夛細1.瑕佹悶娓呮鍒嗚В鑼冨洿锛堝疄鏁拌寖鍥磋繕鏄湁鐞嗘暟鑼冨洿锛屾病鏈夎姹傜殑鏄湁鐞嗘暟鑼冨洿锛夈2.鍒嗚В鍥犲紡瑕佸交搴曪紝鍒嗚В鍒颁笉鑳藉啀鍒嗚В涓烘銆3.鍒嗚В鏃惰涓鎻愶紙鎻愬彇鍏洜寮忥級浜屽锛堝鍏紡锛夛紝涓嶈兘鎻愬拰濂楃殑锛岃鍒嗙粍銆
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绛旓細X^3锛1鍒嗚В鍥犲紡涓(X-1)(X^2+X+1)銆俋^3锛1鍒嗚В鍥犲紡杩囩▼濡備笅锛X^3-1 =X(X^2-1)+(X-1)锛堝姞涓涓猉椤癸紝鍐嶅噺涓涓猉椤癸級=X(X+1)(X-1)+(X-1)锛堝钩鏂瑰樊鍏紡鐨勮繍鐢級=(X-1)(X^2+X+1)锛堟彁鍙朮-1锛
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绛旓細(x-1)(x²+x+1)
绛旓細寰堢畝鍗曪紝(x鍑忎竴锛変箻锛坸^2+x+1)=x^3+x^2+x-x^2-x-1=x^3-1.杩欏氨琛屽暒鍟娿傘
