a+b+c的三次方展开式 a+b的三次方的展开式
\uff08a+b+c+d)\u7684\u4e09\u6b21\u65b9\u7684\u5c55\u5f00\u5f0f\u7684\u9879\u6570\u662f\u591a\u5c11\uff1f\uff08\u6700\u597d\u6709\u8fc7\u7a0b\uff09\u53ef\u4ee5\u628a\u539f\u5f0f\u5199\u6210[(a+b)+(c+d)]^3,\u7136\u540e\u5229\u7528\u6768\u5fbd\u4e09\u89d2\u5c55\u5f00\uff0c\u5c55\u5f00\u5f0f\u4e2d\u51fa\u73b0\u7684\u4e8c\u6b21\u6216\u4e09\u6b21\u65b9\u518d\u8fd0\u7528\u6768\u5fbd\u4e09\u89d2\u5c55\u5f00\uff0c\u6700\u540e\u5c31\u53ef\u4ee5\u5f97\u5230\u4f60\u60f3\u8981\u7684\u7b54\u6848\u4e86\u3002
\u4e5f\u5c31\u662f\uff1a
\u539f\u5f0f=[(a+b)+(c+d)]^3
=[(a+b)+(c+d)]^3=(a+b)^3+3(a+b)^2(c+d)+3(a+b)(c+d)^2+(c+d)^3
\u76f8\u4fe1\u540e\u9762\u7684\u5b8c\u5168OK\u4e86\u5427:-D
（a+b+c）³ =a³+b³+c³+3a²b+3ab²+3b²c+3bc²+3a²c+3ac²+6abc
（a+b+c）³
=（a+b+c）（a+b+c）²
=a³+b³+c³+3a²b+3ab²+3b²c+3bc²+3a²c+3ac²+6abc
扩展资料
其他相关公式：
（1）（a+b）³＝a³＋3a²b＋3ab²＋b³
（2）a³+b³=a³+a²b-a²b+b³=a²（a+b）-b（a²-b²）=a²（a+b）-b（a+b）（a-b）
=（a+b）[a²-b（a-b）]=（a+b）（a²-ab+b²）
（3）a³-b³=a³-a²b+a²b-b³=a²（a-b）+b（a²-b²）=a²（a-b）+b（a+b）（a-b）
=（a-b）[a²+b（a+b）]=（a-b）（a²+ab+b²）
（a+b+c）³ =a³+b³+c³+3a²b+3ab²+3b²c+3bc²+3a²c+3ac²+6abc
解：
(a+b+c)³
=Σ(i,j,k=0,1,2,3且i+j+k=3)[3!/(i!j!k!)]·a^i·b^j·c^k
=a³+b³+c³
+3a²b+3ab²+3a²c+3ac²+3b²c+3bc²
+6abc.
(a+b+c)^3=a^3+b^3+c^3+3a^2b+3ab^2+3a^2c+3ac^2+3b^2c+3bc^2+6abc
(a+b+c)^3=a^3+b^3+c^3+3a^2b+3ab^2+3a^2c+3ac^2+3b^2c+3bc^2+6abc
绛旓細浣嗚繖鏍疯緝绻佺悙銆傛垜浠娇鐢ㄤ簩椤瑰紡瀹氱悊鏉ョ畝鍖栬绠椼傛牴鎹簩椤瑰紡瀹氱悊锛屽浜庝竴涓涓夋鏂鐨勫椤瑰紡锛屽彲浠ヤ娇鐢ㄤ笅闈㈢殑鍏紡鏉ュ睍寮锛(a-b+c)^3 = a^3 - 3a^2b + 3ab^2 - b^3 + 3a^2c - 6abc + 3b^2c + 3ac^2 - 3bc^2 + c^3 杩欐牱锛屾垜浠氨寰楀埌浜哸-b+c鐨勭珛鏂鐨灞曞紑寮銆
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