鍒濅腑鏁板鍥犲紡鍒嗚В
(
涓�
)
鍥犲紡鍒嗚В鏄唬鏁板紡鎭掔瓑鍙樺舰鐨勫熀鏈舰寮忥紝鏄В鍐虫暟瀛﹂棶棰樼殑鏈夊姏宸ュ叿锛庢槸鎺屾彙鍥犲紡鍒嗚В瀵逛簬鍩瑰吇瀛︾敓
瑙ｉ鎶�鑳斤紝鎬濈淮鑳藉姏锛屾湁鐙壒浣滅敤
锛?/p>
1
锛庤繍鐢ㄥ叕寮忔硶
鏁村紡涔樻硶鍏紡锛屽弽鍚戜娇鐢紝鍗充负鍥犲紡鍒嗚В
(1)a
2
-b
2
=(a+b)(a-b)
锛?/p>
(2)a
2
卤
2ab+b
2
=(a
卤
b)
2
锛?/p>
(3)a
3
+b
3
=(a+b)(a
2
-ab+b
2
)
锛?/p>
(4)a
3
-b
3
=(a-b)(a
2
+ab+b
2
)
锛?/p>
鍑犱釜甯哥敤鐨勫叕寮忥細
(5)a
2
+b
2
+c
2
+2ab+2bc+2ca=(a+b+c)
2
锛?/p>
(6)a
3
+b
3
+c
3
-3abc=(a+b+c)(a
2
+b
2
+c
2
-ab-bc-ca)
锛?/p>
(7)a
n
-b
n
=(a-b)(a
n-1
+a
n-2
b+a
n-3
b
2
+
鈥?/p>
+ab
n-2
+b
n-1
)
鍏朵腑
n
涓烘鏁存暟锛?/p>
(8)a
n
-b
n
=(a+b)(a
n-1
-a
n-2
b+a
n-3
b
2
-
鈥?/p>
+ab
n-2
-b
n-1
)
锛屽叾涓?/p>
n
涓哄伓鏁帮紱
(9)a
n
+b
n
=(a+b)(a
n-1
-a
n-2
b+a
n-3
b
2
-
鈥?/p>
-ab
n-2
+b
n-1
)
锛屽叾涓?/p>
n
涓哄鏁帮紟
鍒嗚В鍥犲紡锛屾牴鎹椤瑰紡瀛楁瘝銆佺郴鏁般�佹寚鏁般�佺鍙风瓑姝ｇ‘鎭板綋鍦伴�夋嫨鍏紡锛?/p>
渚?/p>
1
鍒嗚В鍥犲紡锛?/p>
(1)-2x
5n-1
y
n
+4x
3n-1
y
n+2
-2x
n-1
y
n+4
锛?/p>
(2)x
3
-8y
3
-z
3
-6xyz
锛?/p>
(3)a
2
+b
2
+c
2
-2bc+2ca-2ab
锛?/p>
(4)a
7
-a
5
b
2
+a
2
b
5
-b
7
锛?/p>