八年级因式分解用整体法和分组分解法的题目，带答案，越多越好，最好是经典的和提高的，谢谢 求用分组来完成因式分解的题目，如二二分组，三一分组，三二分组
\u56e0\u5f0f\u5206\u89e3\u4e0e\u5206\u7ec4\u5206\u89e3\u8bd5\u9898\u56e0\u5f0f\u5206\u89e3
\u3016\u77e5\u8bc6\u70b9\u3017
\u56e0\u5f0f\u5206\u89e3\u5b9a\u4e49\uff0c\u63d0\u53d6\u516c\u56e0\u5f0f\u3001\u5e94\u7528\u516c\u5f0f\u6cd5\u3001\u5206\u7ec4\u5206\u89e3\u6cd5\u3001\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u56e0\u5f0f\uff08\u5341\u5b57\u76f8\u4e58\u6cd5\u3001\u6c42\u6839\uff09\u3001\u56e0\u5f0f\u5206\u89e3\u4e00\u822c\u6b65\u9aa4\u3002
\u3016\u5927\u7eb2\u8981\u6c42\u3017
\u7406\u89e3\u56e0\u5f0f\u5206\u89e3\u7684\u6982\u5ff5\uff0c\u638c\u63e1\u63d0\u53d6\u516c\u56e0\u5f0f\u6cd5\u3001\u516c\u5f0f\u6cd5\u3001\u5206\u7ec4\u5206\u89e3\u6cd5\u7b49\u56e0\u5f0f\u5206\u89e3\u65b9\u6cd5\uff0c\u638c\u63e1\u5229\u7528\u4e8c\u6b21\u65b9\u7a0b\u6c42\u6839\u516c\u5f0f\u5206\u89e3\u4e8c\u6b21\u4e8c\u9879\u5f0f\u7684\u65b9\u6cd5\uff0c\u80fd\u628a\u7b80\u5355\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u3002
\u3016\u8003\u67e5\u91cd\u70b9\u4e0e\u5e38\u89c1\u9898\u578b\u3017
\u8003\u67e5\u56e0\u5f0f\u5206\u89e3\u80fd\u529b\uff0c\u5728\u4e2d\u8003\u8bd5\u9898\u4e2d\uff0c\u56e0\u5f0f\u5206\u89e3\u51fa\u73b0\u7684\u9891\u7387\u5f88\u9ad8\u3002\u91cd\u70b9\u8003\u67e5\u7684\u5206\u5f0f\u63d0\u53d6\u516c\u56e0\u5f0f\u3001\u5e94\u7528\u516c\u5f0f\u6cd5\u3001\u5206\u7ec4\u5206\u89e3\u6cd5\u53ca\u5b83\u4eec\u7684\u7efc\u5408\u8fd0\u7528\u3002\u4e60\u9898\u7c7b\u578b\u4ee5\u586b\u7a7a\u9898\u4e3a\u591a\uff0c\u4e5f\u6709\u9009\u62e9\u9898\u548c\u89e3\u7b54\u9898\u3002
\u56e0\u5f0f\u5206\u89e3\u77e5\u8bc6\u70b9
\u591a\u9879\u5f0f\u7684\u56e0\u5f0f\u5206\u89e3\uff0c\u5c31\u662f\u628a\u4e00\u4e2a\u591a\u9879\u5f0f\u5316\u4e3a\u51e0\u4e2a\u6574\u5f0f\u7684\u79ef\uff0e\u5206\u89e3\u56e0\u5f0f\u8981\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\uff0e\u5206\u89e3\u56e0\u5f0f\u7684\u5e38\u7528\u65b9\u6cd5\u6709\uff1a
(1)\u63d0\u516c\u56e0\u5f0f\u6cd5
\u5982\u591a\u9879\u5f0f
\u5176\u4e2dm\u53eb\u505a\u8fd9\u4e2a\u591a\u9879\u5f0f\u5404\u9879\u7684\u516c\u56e0\u5f0f\uff0c m\u65e2\u53ef\u4ee5\u662f\u4e00\u4e2a\u5355\u9879\u5f0f\uff0c\u4e5f\u53ef\u4ee5\u662f\u4e00\u4e2a\u591a\u9879\u5f0f\uff0e
(2)\u8fd0\u7528\u516c\u5f0f\u6cd5\uff0c\u5373\u7528
\u5199\u51fa\u7ed3\u679c\uff0e
(3)\u5341\u5b57\u76f8\u4e58\u6cd5
\u5bf9\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\u4e3al\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f \u5bfb\u627e\u6ee1\u8db3ab=q\uff0ca+b=p\u7684a\uff0cb\uff0c\u5982\u6709\uff0c\u5219 \u5bf9\u4e8e\u4e00\u822c\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f \u5bfb\u627e\u6ee1\u8db3
a1a2=a\uff0cc1c2=c,a1c2+a2c1=b\u7684a1\uff0ca2\uff0cc1\uff0cc2\uff0c\u5982\u6709\uff0c\u5219
(4)\u5206\u7ec4\u5206\u89e3\u6cd5\uff1a\u628a\u5404\u9879\u9002\u5f53\u5206\u7ec4\uff0c\u5148\u4f7f\u5206\u89e3\u56e0\u5f0f\u80fd\u5206\u7ec4\u8fdb\u884c\uff0c\u518d\u4f7f\u5206\u89e3\u56e0\u5f0f\u5728\u5404\u7ec4\u4e4b\u95f4\u8fdb\u884c\uff0e
\u5206\u7ec4\u65f6\u8981\u7528\u5230\u6dfb\u62ec\u53f7\uff1a\u62ec\u53f7\u524d\u9762\u662f\u201c+\u201d\u53f7\uff0c\u62ec\u5230\u62ec\u53f7\u91cc\u7684\u5404\u9879\u90fd\u4e0d\u53d8\u7b26\u53f7\uff1b\u62ec\u53f7\u524d\u9762\u662f\u201c-\u201d\u53f7\uff0c\u62ec\u5230\u62ec\u53f7\u91cc\u7684\u5404\u9879\u90fd\u6539\u53d8\u7b26\u53f7.
(5)\u6c42\u6839\u516c\u5f0f\u6cd5\uff1a\u5982\u679c \u6709\u4e24\u4e2a\u6839X1\uff0cX2\uff0c\u90a3\u4e48
\u8003\u67e5\u9898\u578b\uff1a
1\uff0e\u4e0b\u5217\u56e0\u5f0f\u5206\u89e3\u4e2d\uff0c\u6b63\u786e\u7684\u662f\uff08 \uff09���������
(A) 1- 14 x2= 14 (x + 2) (x- 2) (B)4x \u20132 x2 \u2013 2 = - 2(x- 1)2
(C) ( x- y )3 \u2013(y- x) = (x \u2013 y) (x \u2013 y + 1) ( x \u2013y \u2013 1)
(D) x2 \u2013y2 \u2013 x + y = ( x + y) (x \u2013 y \u2013 1)
2\uff0e\u4e0b\u5217\u5404\u7b49\u5f0f(1) a2\uff0d b2 = (a + b) (a\u2013b ),(2) x2\u20133x +2 = x(x\u20133) + 2
(3 ) 1 x2 \u2013y2 \uff0d1 ( x + y) (x \u2013 y ) ,(4 )x2 + 1 x2 \uff0d2\uff0d\uff08 x \uff0d1x )2
\u4ece\u5de6\u5230\u662f\u56e0\u5f0f\u5206\u89e3\u7684\u4e2a\u6570\u4e3a\uff08 \uff09
(A) 1 \u4e2a (B) 2 \u4e2a (C) 3 \u4e2a (D) 4\u4e2a
3\uff0e\u82e5x2\uff0bmx\uff0b25 \u662f\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5219m\u7684\u503c\u662f\uff08 \uff09
(A) 20 (B) 10 (C) \u00b1 20 (D) \u00b110
4\uff0e\u82e5x2\uff0bmx\uff0bn\u80fd\u5206\u89e3\u6210( x+2 ) (x \u2013 5)\uff0c\u5219m= ,n= ;
5\uff0e\u82e5\u4e8c\u6b21\u4e09\u9879\u5f0f2x2+x+5m\u5728\u5b9e\u6570\u8303\u56f4\u5185\u80fd\u56e0\u5f0f\u5206\u89e3\uff0c\u5219m= ;
6\uff0e\u82e5x2+kx\uff0d6\u6709\u4e00\u4e2a\u56e0\u5f0f\u662f(x\uff0d2)\uff0c\u5219k\u7684\u503c\u662f ;
7\uff0e\u628a\u4e0b\u5217\u56e0\u5f0f\u56e0\u5f0f\u5206\u89e3\uff1a
(1)a3\uff0da2\uff0d2a (2)4m2\uff0d9n2\uff0d4m+1
(3)3a2+bc\uff0d3ac-ab (4)9\uff0dx2+2xy\uff0dy2
8\uff0e\u5728\u5b9e\u6570\u8303\u56f4\u5185\u56e0\u5f0f\u5206\u89e3\uff1a
(1)2x2\uff0d3x\uff0d1 (2)\uff0d2x2+5xy+2y2
\u8003\u70b9\u8bad\u7ec3\uff1a
1. \u5206\u89e3\u4e0b\u5217\u56e0\u5f0f\uff1a
(1).10a(x\uff0dy)2\uff0d5b(y\uff0dx) (2).an+1\uff0d4an\uff0b4an-1
(3).x3(2x\uff0dy)\uff0d2x\uff0by (4).x(6x\uff0d1)\uff0d1
(5).2ax\uff0d10ay\uff0b5by\uff0b6x (6).1\uff0da2\uff0dab\uff0d14 b2
*(7).a4\uff0b4 (8).(x2\uff0bx)(x2\uff0bx\uff0d3)\uff0b2
(9).x5y\uff0d9xy5 (10).\uff0d4x2\uff0b3xy\uff0b2y2
(11).4a\uff0da5 (12).2x2\uff0d4x\uff0b1
(13).4y2\uff0b4y\uff0d5 (14)3X2\uff0d7X+2
\u89e3\u9898\u6307\u5bfc\uff1a
1\uff0e\u4e0b\u5217\u8fd0\u7b97:(1) (a\uff0d3)2\uff1da2\uff0d6a\uff0b9 (2) x\uff0d4\uff1d(x \uff0b2)( x \uff0d2)
(3) ax2\uff0ba2xy\uff0ba\uff1da(x2\uff0bax) (4) 116 x2\uff0d14 x\uff0b14 \uff1dx2\uff0d4x\uff0b4\uff1d(x\uff0d2)2\u5176\u4e2d\u662f\u56e0\u5f0f\u5206\u89e3\uff0c\u4e14\u8fd0\u7b97\u6b63\u786e\u7684\u4e2a\u6570\u662f\uff08 \uff09
\uff08A\uff091 \uff08B\uff092 \uff08C\uff093 \uff08D\uff094
2\uff0e\u4e0d\u8bbaa\u4e3a\u4f55\u503c\uff0c\u4ee3\u6570\u5f0f\uff0da2\uff0b4a\uff0d5\u503c\uff08 \uff09
\uff08A\uff09\u5927\u4e8e\u6216\u7b49\u4e8e0 \uff08B\uff090 \uff08C\uff09\u5927\u4e8e0 \uff08D\uff09\u5c0f\u4e8e0
3\uff0e\u82e5x2\uff0b2\uff08m\uff0d3\uff09x\uff0b16 \u662f\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5219m\u7684\u503c\u662f\uff08 \uff09
\uff08A\uff09\uff0d5 \uff08B\uff097 \uff08C\uff09\uff0d1 \uff08D\uff097\u6216\uff0d1
4\uff0e(x2\uff0by2)(x2\uff0d1\uff0by2)\uff0d12\uff1d0,\u5219x2\uff0by2\u7684\u503c\u662f \uff1b
5\uff0e\u5206\u89e3\u4e0b\u5217\u56e0\u5f0f\uff1a
(1).8xy(x\uff0dy)\uff0d2(y\uff0dx)3 \uff0a(2).x6\uff0dy6
(3).x3\uff0b2xy\uff0dx\uff0dxy2 \uff0a(4).(x\uff0by)(x\uff0by\uff0d1)\uff0d12
(5).4ab\uff0d\uff081\uff0da2\uff09\uff081\uff0db2\uff09 (6).\uff0d3m2\uff0d2m\uff0b4
\uff0a4\u3002\u5df2\u77e5a\uff0bb\uff1d1,\u6c42a3\uff0b3ab\uff0bb3\u7684\u503c
5\uff0ea\u3001b\u3001c\u4e3a\u22bfABC\u4e09\u8fb9\uff0c\u5229\u7528\u56e0\u5f0f\u5206\u89e3\u8bf4\u660eb2\uff0da2\uff0b2ac\uff0dc2\u7684\u7b26\u53f7
6\uff0e0\uff1ca\u22645\uff0ca\u4e3a\u6574\u6570\uff0c\u82e52x2\uff0b3x\uff0ba\u80fd\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u6c42\u7b26\u5408\u6761\u4ef6\u7684a
\u72ec\u7acb\u8bad\u7ec3\uff1a
1\uff0e\u591a\u9879\u5f0fx2\uff0dy2, x2\uff0d2xy\uff0by2, x3\uff0dy3\u7684\u516c\u56e0\u5f0f\u662f \u3002
2\uff0e\u586b\u4e0a\u9002\u5f53\u7684\u6570\u6216\u5f0f\uff0c\u4f7f\u5de6\u8fb9\u53ef\u5206\u89e3\u4e3a\u53f3\u8fb9\u7684\u7ed3\u679c\uff1a
(1)9x2\uff0d( )2\uff1d(3x\uff0b )( \uff0d15 y), (2).5x2\uff0b6xy\uff0d8y2\uff1d(x )( \uff0d4y).
3\uff0e\u77e9\u5f62\u7684\u9762\u79ef\u4e3a6x2\uff0b13x\uff0b5 (x>0),\u5176\u4e2d\u4e00\u8fb9\u957f\u4e3a2x\uff0b1,\u5219\u53e6\u4e3a \u3002
4\uff0e\u628aa2\uff0da\uff0d6\u5206\u89e3\u56e0\u5f0f\uff0c\u6b63\u786e\u7684\u662f( )
(A)a(a\uff0d1)\uff0d6 (B)(a\uff0d2)(a\uff0b3) (C)(a\uff0b2)(a\uff0d3) (D)(a\uff0d1)(a\uff0b6)
5\uff0e\u591a\u9879\u5f0fa2\uff0b4ab\uff0b2b2,a2\uff0d4ab\uff0b16b2,a2\uff0ba\uff0b14 ,9a2\uff0d12ab\uff0b4b2\u4e2d\uff0c\u80fd\u7528\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u6709( )
(A) 1\u4e2a (B) 2\u4e2a (C) 3\u4e2a (D) 4\u4e2a
6\uff0e\u8bbe(x\uff0by)(x\uff0b2\uff0by)\uff0d15\uff1d0,\u5219x\uff0by\u7684\u503c\u662f\uff08 \uff09
(A)-5\u62163 (B) -3\u62165 (C)3 (D)5
7\uff0e\u5173\u4e8e\u7684\u4e8c\u6b21\u4e09\u9879\u5f0fx2\uff0d4x\uff0bc\u80fd\u5206\u89e3\u6210\u4e24\u4e2a\u6574\u7cfb\u6570\u7684\u4e00\u6b21\u7684\u79ef\u5f0f\uff0c\u90a3\u4e48c\u53ef\u53d6\u4e0b\u9762\u56db\u4e2a\u503c\u4e2d\u7684\uff08 \uff09
(A) \uff0d8 (B) \uff0d7 (C) \uff0d6 (D) \uff0d5
8\uff0e\u82e5x2\uff0dmx\uff0bn\uff1d(x\uff0d4)(x\uff0b3) \u5219m,n\u7684\u503c\u4e3a\uff08 \uff09
(A) m\uff1d\uff0d1, n\uff1d\uff0d12 (B)m\uff1d\uff0d1,n\uff1d12 (C) m\uff1d1,n\uff1d\uff0d12 (D) m\uff1d1,n\uff1d12.
9\uff0e\u4ee3\u6570\u5f0fy2\uff0bmy\uff0b254 \u662f\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u5219m\u7684\u503c\u662f \u3002
10\uff0e\u5df2\u77e52x2\uff0d3xy\uff0by2\uff1d0\uff08x,y\u5747\u4e0d\u4e3a\u96f6\uff09\uff0c\u5219 xy \uff0b yx \u7684\u503c\u4e3a \u3002
11\uff0e\u5206\u89e3\u56e0\u5f0f:
(1).x2(y\uff0dz)\uff0b81(z\uff0dy) (2).9m2\uff0d6m\uff0b2n\uff0dn2
\uff0a(3).ab(c2\uff0bd2)\uff0bcd(a2\uff0bb2) (4).a4\uff0d3a2\uff0d4
\uff0a(5).x4\uff0b4y4 \uff0a(6).a2\uff0b2ab\uff0bb2\uff0d2a\uff0d2b\uff0b1
12\uff0e\u5b9e\u6570\u8303\u56f4\u5185\u56e0\u5f0f\u5206\u89e3
\uff081\uff09x2\uff0d2x\uff0d4 \uff082\uff094x2\uff0b8x\uff0d1 \uff083\uff092x2\uff0b4xy\uff0by2
\u5206\u7ec4\u5206\u89e3\u6cd5\uff1a\u628a\u5404\u9879\u9002\u5f53\u5206\u7ec4\uff0c\u5148\u4f7f\u5206\u89e3\u56e0\u5f0f\u80fd\u5206\u7ec4\u8fdb\u884c\uff0c\u518d\u4f7f\u5206\u89e3\u56e0\u5f0f\u5728\u5404\u7ec4\u4e4b\u95f4\u8fdb\u884c\uff0e
\u5206\u7ec4\u65f6\u8981\u7528\u5230\u6dfb\u62ec\u53f7\uff1a\u62ec\u53f7\u524d\u9762\u662f\u201c+\u201d\u53f7\uff0c\u62ec\u5230\u62ec\u53f7\u91cc\u7684\u5404\u9879\u90fd\u4e0d\u53d8\u7b26\u53f7\uff1b\u62ec\u53f7\u524d\u9762\u662f\u201c-\u201d\u53f7\uff0c\u62ec\u5230\u62ec\u53f7\u91cc\u7684\u5404\u9879\u90fd\u6539\u53d8\u7b26\u53f7.
\u5f53\u591a\u9879\u5f0f\u7684\u9879\u6570\u8f83\u591a\u65f6\uff0c\u53ef\u5c06\u591a\u9879\u5f0f\u8fdb\u884c\u5408\u7406\u5206\u7ec4\uff0c\u8fbe\u5230\u987a\u5229\u5206\u89e3\u7684\u76ee\u7684\u3002\u5f53\u7136\u53ef\u80fd\u8981\u7efc\u5408\u5176\u4ed6\u5206\u6cd5\uff0c\u4e14\u5206\u7ec4\u65b9\u6cd5\u4e5f\u4e0d\u4e00\u5b9a\u552f\u4e00\u3002
\u4f8b1\u5206\u89e3\u56e0\u5f0f\uff1ax15+m12+m9+m6+m3+1
\u89e3\u539f\u5f0f=\uff08x15+m12\uff09+(m9+m6)+(m3+1)
=m12(m3+1)+m6(m3+1)+(m3+1)
=(m3+1)(m12+m6++1)
=(m3+1)[(m6+1)2-m6]
=(m+1)(m2-m+1)(m6+1+m3)(m6+1-m3)
\u4f8b2\u5206\u89e3\u56e0\u5f0f\uff1ax4+5x3+15x-9
\u89e3\u6790\u53ef\u6839\u636e\u7cfb\u6570\u7279\u5f81\u8fdb\u884c\u5206\u7ec4
\u89e3\u539f\u5f0f=\uff08x4-9\uff09+5x3+15x
=(x2+3)(x2-3)+5x(x2+3)
=(x2+3)(x2+5x-3)
\u201c\u5206\u7ec4\u5206\u89e3\u6cd5\u201d\u4e2d\u7684\u201c\u4e8c\u4e8c\u5206\u6cd5\u201d\u5982\uff1a \u2460x??-xy+4x-4y \u2461x??+3x??-4x-12 \u24624a??-b??+6a-3b
=x(x-y\uff09+4\uff08x-y\uff09 =x??(x+3)-4(x+3\uff09 =(2a+b)(2a-b)+3(2a-b)
=(x+4)(x-y) =\uff08x??-4\uff09(x+3\uff09 =(2a+b+3)(2a-b)
\u201c\u5206\u7ec4\u5206\u89e3\u6cd5\u201d\u4e2d\u7684\u201c\u4e09\u4e00\u5206\u6cd5\u201d\u5982\uff1a
\u2460a??-b??-c??+2bc \u2461x??-y??-4x+4 \u24629a??-4b??+4bc-c??
=a??-(b??+c??-2bc) =(x??-4x+4)-y?? =9a??-(4a??-4bc+c??)
=a??-(b-c)?? =(x-2)??-y?? =9a??-(2b-c)??
=(a+b-c)(a-b+c) =(x+y-2)(x-y-2) =(3a+2b-c)(3a-2b+c)
\u201c\u5206\u7ec4\u5206\u89e3\u6cd5\u201d\u4e2d\u7684\u201c\u4e09\u4e8c\u4e00\u5206\u6cd5\u201d\u5982\uff1a
\u2460a??-2ab+b??+3a-3b+2
=(a??-2ab+b??)+(3a-3b)+2
=(a-b)??+3(a-b)+2
=(a-b+1)(a-b+2)
\u6ce8\u610f\uff1a\u03c7??\u6216\u03b1??\u6216\u03c7??\u7b49\uff0c\u5b83\u4eec\u4e2d\u540e\u9762\u7684\u6570\u5b57\u662f\u672a\u77e5\u6570\u7684\u5e42\uff08\u4e5f\u5c31\u662f\u591a\u5c11\u6b21\u65b9\uff01\uff01\uff01\uff09
\u4f60\u6709\u4e0d\u61c2\u7684\u53ef\u4ee5\u6765\u95ee\u6211\uff01\uff01\uff01
\u5f90\u4e16\u5947
2.4m的平方+8m+4
3.(x的平方+4）的平方+8x(x的平方+4）+16x的平方）
4.已知(a+2b)的平方-2a-4b+1=0，求(a+b)的2006次方
5.9a的平方-4b的平方+4bc-c的平方
6.8a的三次方b的三次方c的三次方-1
因式分解3a3b2c－6a2b2c2＋9ab2c3＝3ab^2 c(a^2-2ac+3c^2)
3.因式分解xy＋6－2x－3y＝(x-3)(y-2)
4.因式分解x2(x－y)＋y2(y－x)＝(x+y)(x-y)^2
5.因式分解2x2－(a－2b)x－ab＝(2x-a)(x+b)
6.因式分解a4－9a2b2＝a^2(a+3b)(a-3b)
7.若已知x3＋3x2－4含有x－1的因式，试分解x3＋3x2－4＝(x-1)(x+2)^2
8.因式分解ab(x2－y2)＋xy(a2－b2)＝(ay+bx)(ax-by)
9.因式分解(x＋y)(a－b－c)＋(x－y)(b＋c－a)＝2y(a-b-c)
10.因式分解a2－a－b2－b＝(a+b)(a-b-1)
11.因式分解(3a－b)2－4(3a－b)(a＋3b)＋4(a＋3b)2＝[3a-b-2(a+3b)]^2=(a-7b)^2
12.因式分解(a＋3)2－6(a＋3)＝(a+3)(a-3)
13.因式分解(x＋1)2(x＋2)－(x＋1)(x＋2)2＝-(x+1)(x+2)
abc＋ab－4a＝a(bc+b-4)
(2)16x2－81＝(4x+9)(4x-9)
(3)9x2－30x＋25＝(3x-5)^2
(4)x2－7x－30＝(x-10)(x+3)
35.因式分解x2－25＝(x+5)(x-5)
36.因式分解x2－20x＋100＝(x-10)^2
37.因式分解x2＋4x＋3＝(x+1)(x+3)
38.因式分解4x2－12x＋5＝(2x-1)(2x-5)
39.因式分解下列各式：
(1)3ax2－6ax＝3ax(x-2)
(2)x(x＋2)－x＝x(x+1)
(3)x2－4x－ax＋4a＝(x-4)(x-a)
(4)25x2－49＝(5x-9)(5x+9)
(5)36x2－60x＋25＝(6x-5)^2
(6)4x2＋12x＋9＝(2x+3)^2
(7)x2－9x＋18＝(x-3)(x-6)
(8)2x2－5x－3＝(x-3)(2x+1)
(9)12x2－50x＋8＝2(6x-1)(x-4)
40.因式分解(x＋2)(x－3)＋(x＋2)(x＋4)＝(x+2)(2x-1)
41.因式分解2ax2－3x＋2ax－3＝ (x+1)(2ax-3)
42.因式分解9x2－66x＋121＝(3x-11)^2
43.因式分解8－2x2＝2(2+x)(2-x)
44.因式分解x2－x＋14 ＝整数内无法分解
45.因式分解9x2－30x＋25＝(3x-5)^2
46.因式分解－20x2＋9x＋20＝(-4x+5)(5x+4)
47.因式分解12x2－29x＋15＝(4x-3)(3x-5)
48.因式分解36x2＋39x＋9＝3(3x+1)(4x+3)
49.因式分解21x2－31x－22＝(21x+11)(x-2)
50.因式分解9x4－35x2－4＝(9x^2+1)(x+2)(x-2)
51.因式分解(2x＋1)(x＋1)＋(2x＋1)(x－3)＝2(x-1)(2x+1)
52.因式分解2ax2－3x＋2ax－3＝(x+1)(2ax-3)
53.因式分解x(y＋2)－x－y－1＝(x-1)(y+1)
54.因式分解(x2－3x)＋(x－3)2＝(x-3)(2x-3)
55.因式分解9x2－66x＋121＝(3x-11)^2
56.因式分解8－2x2＝2(2-x)(2+x)
57.因式分解x4－1＝(x-1)(x+1)(x^2+1)
58.因式分解x2＋4x－xy－2y＋4＝(x+2)(x-y+2)
59.因式分解4x2－12x＋5＝(2x-1)(2x-5)
60.因式分解21x2－31x－22＝(21x+11)(x-2)
61.因式分解4x2＋4xy＋y2－4x－2y－3＝(2x+y-3)(2x+y+1)
62.因式分解9x5－35x3－4x＝x(9x^2+1)(x+2)(x-2)
63.因式分解下列各式：
(1)3x2－6x＝3x(x-2)
(2)49x2－25＝(7x+5)(7x-5)
(3)6x2－13x＋5＝(2x-1)(3x-5)
(4)x2＋2－3x＝(x-1)(x-2)
(5)12x2－23x－24＝(3x-8)(4x+3)
(6)(x＋6)(x－6)－(x－6)＝(x-6)(x+5)
(7)3(x＋2)(x－5)－(x＋2)(x－3)＝2(x-6)(x+2)
(8)9x2＋42x＋49＝(3x+7)^2
(1)-2x5n-1yn+4x3n-1yn+2-2xn-1yn+4；
(2)x3-8y3-z3-6xyz；
(3)a2+b2+c2-2bc+2ca-2ab；
(4)a7-a5b2+a2b5-b7．
解 (1)原式=-2xn-1yn(x4n-2x2ny2+y4)
=-2xn-1yn[(x2n)2-2x2ny2+(y2)2]
=-2xn-1yn(x2n-y2)2
=-2xn-1yn(xn-y)2(xn+y)2．
(2)原式=x3+(-2y)3+(-z)3-3x(-2y)(-Z)
=(x-2y-z)(x2+4y2+z2+2xy+xz-2yz)．
(3)原式=(a2-2ab+b2)+(-2bc+2ca)+c2
＝(a-b)2+2c(a-b)+c2
=(a-b+c)2．
(4)原式=(a7-a5b2)+(a2b5-b7)
=a5(a2-b2)+b5(a2-b2)
=(a2-b2)(a5+b5)
=(a+b)(a-b)(a+b)(a4-a3b+a2b2-ab3+b4)
=(a+b)2(a-b)(a4-a3b+a2b2-ab3+b4)
分解因式：
(1)x9+x6+x3-3；
(2)(m2-1)(n2-1)+4mn；
(3)(x+1)4+(x2-1)2+(x-1)4；
(4)a3b-ab3+a2+b2+1．
解 (1)将-3拆成-1-1-1．
原式=x9+x6+x3-1-1-1
=(x9-1)+(x6-1)+(x3-1)
=(x3-1)(x6+x3+1)+(x3-1)(x3+1)+(x3-1)
=(x3-1)(x6+2x3+3)
=(x-1)(x2+x+1)(x6+2x3+3)．
(2)将4mn拆成2mn+2mn．
原式=(m2-1)(n2-1)+2mn+2mn
=m2n2-m2-n2+1+2mn+2mn
=(m2n2+2mn+1)-(m2-2mn+n2)
=(mn+1)2-(m-n)2
=(mn+m-n+1)(mn-m+n+1)．
(3)将(x2-1)2拆成2(x2-1)2-(x2-1)2．
原式=(x+1)4+2(x2-1)2-(x2-1)2+(x-1)4
=〔(x+1)4+2(x+1)2(x-1)2+(x-1)4]-(x2-1)2
=〔(x+1)2+(x-1)2]2-(x2-1)2
=(2x2+2)2-(x2-1)2=(3x2+1)(x2+3)．
(4)添加两项+ab-ab．
原式=a3b-ab3+a2+b2+1+ab-ab
=(a3b-ab3)+(a2-ab)+(ab+b2+1)
=ab(a+b)(a-b)+a(a-b)+(ab+b2+1)
=a(a-b)〔b(a+b)+1]+(ab+b2+1)
=[a(a-b)+1](ab+b2+1)
=(a2-ab+1)(b2+ab+1)．
(1)-2x5n-1yn+4x3n-1yn+2-2xn-1yn+4；
(2)x3-8y3-z3-6xyz；
(3)a2+b2+c2-2bc+2ca-2ab；
(4)a7-a5b2+a2b5-b7．
解 (1)原式=-2xn-1yn(x4n-2x2ny2+y4)
=-2xn-1yn[(x2n)2-2x2ny2+(y2)2]
=-2xn-1yn(x2n-y2)2
=-2xn-1yn(xn-y)2(xn+y)2．
(2)原式=x3+(-2y)3+(-z)3-3x(-2y)(-Z)
=(x-2y-z)(x2+4y2+z2+2xy+xz-2yz)．
(3)原式=(a2-2ab+b2)+(-2bc+2ca)+c2
＝(a-b)2+2c(a-b)+c2
=(a-b+c)2．
本小题可以稍加变形，直接使用公式(5)，解法如下：
原式=a2+(-b)2+c2+2(-b)c+2ca+2a(-b)
=(a-b+c)2
(4)原式=(a7-a5b2)+(a2b5-b7)
=a5(a2-b2)+b5(a2-b2)
=(a2-b2)(a5+b5)
=(a+b)(a-b)(a+b)(a4-a3b+a2b2-ab3+b4)
=(a+b)2(a-b)(a4-a3b+a2b2-ab3+b4)
(1)x9+x6+x3-3；
(2)(m2-1)(n2-1)+4mn；
(3)(x+1)4+(x2-1)2+(x-1)4；
(4)a3b-ab3+a2+b2+1．
解 (1)将-3拆成-1-1-1．
原式=x9+x6+x3-1-1-1
=(x9-1)+(x6-1)+(x3-1)
=(x3-1)(x6+x3+1)+(x3-1)(x3+1)+(x3-1)
=(x3-1)(x6+2x3+3)
=(x-1)(x2+x+1)(x6+2x3+3)．
(2)将4mn拆成2mn+2mn．
原式=(m2-1)(n2-1)+2mn+2mn
=m2n2-m2-n2+1+2mn+2mn
=(m2n2+2mn+1)-(m2-2mn+n2)
=(mn+1)2-(m-n)2
=(mn+m-n+1)(mn-m+n+1)．
(3)将(x2-1)2拆成2(x2-1)2-(x2-1)2．
原式=(x+1)4+2(x2-1)2-(x2-1)2+(x-1)4
=〔(x+1)4+2(x+1)2(x-1)2+(x-1)4]-(x2-1)2
=〔(x+1)2+(x-1)2]2-(x2-1)2
=(2x2+2)2-(x2-1)2=(3x2+1)(x2+3)．
(4)添加两项+ab-ab．
原式=a3b-ab3+a2+b2+1+ab-ab
=(a3b-ab3)+(a2-ab)+(ab+b2+1)
=ab(a+b)(a-b)+a(a-b)+(ab+b2+1)
=a(a-b)〔b(a+b)+1]+(ab+b2+1)
=[a(a-b)+1](ab+b2+1)
=(a2-ab+1)(b2+ab+1)．
1．分解因式：
(2)x10+x5-2；
(4)(x5+x4+x3+x2+x+1)2-x5．
2．分解因式：
(1)x3+3x2-4；
(2)x4-11x2y2+y2；
(3)x3+9x2+26x+24；
(4)x4-12x+323．
3．分解因式：
(1)(2x2-3x+1)2-22x2+33x-1；
(2)x4+7x3+14x2+7x+1；
(3)(x+y)3+2xy(1-x-y)-1；
(4)(x+3)(x2-1)(x+5)-20．
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