数学的十字相乘怎么分解 数学上的十字相乘分解因式怎么用啊？
\u6570\u5b66\u56e0\u5f0f\u5206\u89e3\u7684\u5341\u5b57\u76f8\u4e58\u6cd5\u662f\u600e\u6837\u505a\u7684\u7b80\u5355\u7684\u8bf4\uff0c\u5341\u5b57\u76f8\u4e58\u7684\u539f\u7406 \u662f\u6839\u636e \u5206\u89e3\u56e0\u5f0f\u3002
\u5373\uff08ax+b\uff09(cx+d)=acx^2+(bc+ad)x+bd
\u5341\u5b57\u76f8\u4e58 \u5341\u5b57\u76f8\u4e58\u6cd5\u867d\u7136\u6bd4\u8f83\u96be\u5b66,\u4f46\u662f\u4e00\u65e6\u5b66\u4f1a\u4e86\u5b83,\u7528\u5b83\u6765\u89e3\u9898,\u4f1a\u7ed9\u6211\u4eec\u5e26\u6765\u5f88\u591a\u65b9\u4fbf,\u4ee5\u4e0b\u662f\u5341\u5b57\u76f8\u4e58\u6cd5\u3002
1\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u65b9\u6cd5\uff1a\u5341\u5b57\u5de6\u8fb9\u76f8\u4e58\u7b49\u4e8e\u4e8c\u6b21\u9879\u7cfb\u6570\uff0c\u53f3\u8fb9\u76f8\u4e58\u7b49\u4e8e\u5e38\u6570\u9879\uff0c\u4ea4\u53c9\u76f8\u4e58\u518d\u76f8\u52a0\u7b49\u4e8e\u4e00\u6b21\u9879\u7cfb\u6570\u3002
2\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7528\u5904\uff1a\uff081\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\u56e0\u5f0f\u3002\uff082\uff09\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u4e00\u5143\u4e8c\u6b21\u65b9\u7a0b\u3002
3\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u4f18\u70b9\uff1a\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u9898\u7684\u901f\u5ea6\u6bd4\u8f83\u5feb\uff0c\u80fd\u591f\u8282\u7ea6\u65f6\u95f4\uff0c\u800c\u4e14\u8fd0\u7528\u7b97\u91cf\u4e0d\u5927\uff0c\u4e0d\u5bb9\u6613\u51fa\u9519\u3002
4\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u7684\u7f3a\u9677\uff1a1\u3001\u6709\u4e9b\u9898\u76ee\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u6bd4\u8f83\u7b80\u5355\uff0c\u4f46\u5e76\u4e0d\u662f\u6bcf\u4e00\u9053\u9898\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u89e3\u90fd\u7b80\u5355\u30022\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u53ea\u9002\u7528\u4e8e\u4e8c\u6b21\u4e09\u9879\u5f0f\u7c7b\u578b\u7684\u9898\u76ee\u30023\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6bd4\u8f83\u96be\u5b66\u3002
5\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u9898\u5b9e\u4f8b\uff1a
1)\u3001 \u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u7b80\u5355\u5e38\u89c1\u7684\u9898\u76ee
\u4f8b1\u628am²+4m-12\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u5e38\u6570\u9879-12\u53ef\u4ee5\u5206\u4e3a-1\u00d712\uff0c-2\u00d76\uff0c-3\u00d74\uff0c-4\u00d73\uff0c-6\u00d72\uff0c-12\u00d71\u5f53-12\u5206\u6210-2\u00d76\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a\u56e0\u4e3a 1 -2
1 \u2573 6
\u6240\u4ee5m²+4m-12=\uff08m-2\uff09\uff08m+6\uff09
\u4f8b2\u628a5²+6x-8\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u672c\u9898\u4e2d\u76845\u53ef\u5206\u4e3a1\u00d75,-8\u53ef\u5206\u4e3a-1\u00d78\uff0c-2\u00d74\uff0c-4\u00d72\uff0c-8\u00d71\u3002\u5f53\u4e8c\u6b21\u9879\u7cfb\u6570\u5206\u4e3a1\u00d75\uff0c\u5e38\u6570\u9879\u5206\u4e3a-4\u00d72\u65f6\uff0c\u624d\u7b26\u5408\u672c\u9898
\u89e3\uff1a \u56e0\u4e3a 1 2
5 \u2573 -4
\u6240\u4ee55²+6x-8=\uff08x+2\uff09\uff085x-4\uff09
\u4f8b3\u89e3\u65b9\u7a0bx²-8x+15=0
\u5206\u6790\uff1a\u628ax²-8x+15\u770b\u6210\u5173\u4e8ex\u7684\u4e00\u4e2a\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u521915\u53ef\u5206\u62101\u00d715\uff0c3\u00d75\u3002
\u89e3\uff1a \u56e0\u4e3a 1 -3
1 \u2573 -5
\u6240\u4ee5\u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\uff08x-3\uff09\uff08x-5\uff09=0
\u6240\u4ee5x1=3 x2=5
\u4f8b4\u3001\u89e3\u65b9\u7a0b 6²-5x-25=0
\u5206\u6790\uff1a\u628a6²5x-25\u770b\u6210\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\uff0c\u52196\u53ef\u4ee5\u5206\u4e3a1\u00d76\uff0c2\u00d73\uff0c-25\u53ef\u4ee5\u5206\u6210-1\u00d725\uff0c-5\u00d75\uff0c-25\u00d71\u3002
\u89e3\uff1a \u56e0\u4e3a 2 -5
3 \u2573 5
\u6240\u4ee5 \u539f\u65b9\u7a0b\u53ef\u53d8\u5f62\u6210\uff082x-5\uff09\uff083x+5\uff09=0
\u6240\u4ee5 x1=5/2 x2=-5/3
2)\u3001\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u89e3\u4e00\u4e9b\u6bd4\u8f83\u96be\u7684\u9898\u76ee
\u4f8b5\u628a14²-67xy+18y²\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u628a14x²-67xy+18y²\u770b\u6210\u662f\u4e00\u4e2a\u5173\u4e8ex\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f,\u521914\u53ef\u5206\u4e3a1\u00d714,2\u00d77, 18y²\u53ef\u5206\u4e3ay.18y , 2y.9y , 3y.6y
\u89e3: \u56e0\u4e3a 2 -9y
7 \u2573 -2y
\u6240\u4ee5 14x²-67xy+18y²= (2x-2y)(7x-9y)
\u4f8b6 \u628a10x²-27xy-28y²-x+25y-3\u5206\u89e3\u56e0\u5f0f
\u5206\u6790\uff1a\u5728\u672c\u9898\u4e2d\uff0c\u8981\u628a\u8fd9\u4e2a\u591a\u9879\u5f0f\u6574\u7406\u6210\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u5f62\u5f0f
\u89e3\u6cd5\u4e00\u300110x²-27xy-28y²-x+25y-3
=10x²-\uff0827y+1\uff09x -\uff0828y²;-25y+3\uff09
4y -3
7y \u2573 -1
=10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09
=[2x -\uff087y -1\uff09][5x +\uff084y -3\uff09] 2 -\uff087y \u2013 1\uff09
5 \u2573 4y - 3
=\uff082x -7y +1\uff09\uff085x +4y -3\uff09
\u8bf4\u660e\uff1a\u5728\u672c\u9898\u4e2d\u5148\u628a28y²-25y+3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff084y-3\uff09\uff087y -1\uff09\uff0c\u518d\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a10x²-\uff0827y+1\uff09x -\uff084y-3\uff09\uff087y -1\uff09\u5206\u89e3\u4e3a[2x -\uff087y -1\uff09][5x +\uff084y+3\uff09]
\u89e3\u6cd5\u4e8c\u300110x²-27xy-28y²-x+25y-3
=\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3 2 -7y
=[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3] 5 \u2573 4y
=\uff082x -7y+1\uff09\uff085x -4y -3\uff09 2 x -7y 1
5 x - 4y \u2573 -3
\u8bf4\u660e:\u5728\u672c\u9898\u4e2d\u5148\u628a10x²-27xy-28y²\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a\uff082x -7y\uff09\uff085x +4y\uff09,\u518d\u628a\uff082x -7y\uff09\uff085x +4y\uff09-\uff08x -25y\uff09- 3\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u4e3a[\uff082x -7y\uff09+1] [\uff085x -4y\uff09-3].
\u4f8b7\uff1a\u89e3\u5173\u4e8ex\u65b9\u7a0b\uff1ax²- 3ax + 2a²\u2013ab -b²=0
\u5206\u6790\uff1a2a²\u2013ab-b²\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3
\u89e3\uff1ax²- 3ax + 2a²\u2013ab -b²=0
x²- 3ax +\uff082a²\u2013ab - b²\uff09=0
x²- 3ax +\uff082a+b\uff09\uff08a-b\uff09=0 1 -b
2 \u2573 +b
[x-\uff082a+b\uff09][ x-\uff08a-b\uff09]=0 1 -\uff082a+b\uff09
1 \u2573 -\uff08a-b\uff09
\u6240\u4ee5 x1=2a+b x2=a-b
\u6ce8\u610f
1.\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u628a\u67d0\u4e9b\u5f62\u5982ax2+bx+c\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u5e94\u6ce8\u610f\u4ee5\u4e0b\u95ee\u9898\uff1a
(1)\u6b63\u786e\u7684\u5341\u5b57\u76f8\u4e58\u5fc5\u987b\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a
a1 c1
\u5728\u5f0f\u5b50 � \u4e2d\uff0c\u7ad6\u5411\u7684\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1a2=a\uff0cc1c2=c\uff1b\u5728\u4e0a\u5f0f\u4e2d\uff0c\u659c\u5411\u7684
a2 c2
\u4e24\u4e2a\u6570\u5fc5\u987b\u6ee1\u8db3\u5173\u7cfba1c2+a2c1=b.
(2)\u7531\u5341\u5b57\u76f8\u4e58\u7684\u56fe\u4e2d\u7684\u56db\u4e2a\u6570\u5199\u51fa\u5206\u89e3\u540e\u7684\u4e24\u4e2a\u4e00\u6b21\u56e0\u5f0f\u65f6\uff0c\u56fe\u7684\u4e0a\u4e00\u884c\u4e24\u4e2a\u6570\u4e2d\uff0ca1\u662f\u7b2c\u4e00\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7cfb\u6570\uff0cc1\u662f\u5e38\u6570\u9879\uff1b\u5728\u4e0b\u4e00\u884c\u7684\u4e24\u4e2a\u6570\u4e2d\uff0ca2\u662f\u7b2c\u4e8c\u4e2a\u56e0\u5f0f\u4e2d\u7684\u4e00\u6b21\u9879\u7684\u7cfb\u6570\uff0cc2\u662f\u5e38\u6570\u9879.
(3)\u4e8c\u6b21\u9879\u7cfb\u6570a\u4e00\u822c\u90fd\u628a\u5b83\u770b\u4f5c\u662f\u6b63\u6570(\u5982\u679c\u662f\u8d1f\u6570\uff0c\u5219\u5e94\u63d0\u51fa\u8d1f\u53f7\uff0c\u5229\u7528\u6052\u7b49\u53d8\u5f62\u628a\u5b83\u8f6c\u5316\u4e3a\u6b63\u6570\uff0c)\u53ea\u9700\u628a\u5b83\u5206\u89e3\u6210\u4e24\u4e2a\u6b63\u7684\u56e0\u6570.
2.\u5f62\u5982x+px+q\u7684\u67d0\u4e9b\u4e8c\u6b21\u4e09\u9879\u5f0f\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f.
3.\u51e1\u662f\u53ef\u7528\u4ee3\u6362\u7684\u65b9\u6cd5\u8f6c\u5316\u4e3a\u4e8c\u6b21\u4e09\u9879\u5f0fax+bx+c\u7684\u591a\u9879\u5f0f\uff0c\u6709\u4e9b\u4e5f\u53ef\u4ee5\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e3\u56e0\u5f0f\uff0c\u5982\u4f8b4.
把 二次项系数 a分解成两个因数a1,a2的积a1·a2，把常数项c分解成两个因数c1,c2的积c1·c2
如x^2+4x-5=0的x=-1或x=5分解如下：
x -5
x 1
其实就是把平方项分解因数
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绛旓細鍐嶇浉鍔狅紝寰楀埌a1c2+a2c1锛岃嫢瀹冩濂界瓑浜庝簩娆′笁椤瑰紡ax2+bx+c鐨勪竴娆￠」绯绘暟b锛屽嵆a1c2+a2c1=b锛岄偅涔堜簩娆′笁椤瑰紡灏卞彲浠鍒嗚В涓轰袱涓洜寮廰1x+c1涓巃2x+c2涔嬬Н锛屽嵆 ax2+bx+c=(a1x+c1)(a2x+c2).鍍忚繖绉嶅熷姪鐢诲崄瀛椾氦鍙夌嚎鍒嗚В绯绘暟锛屼粠鑰屽府鍔╂垜浠妸浜屾涓夐」寮忓垎瑙ｅ洜寮忕殑鏂规硶锛岄氬父鍙仛鍗佸瓧鐩镐箻娉.
绛旓細鍗佸瓧鍒嗚В娉曠殑鏂规硶绠鍗曟潵璁插氨鏄細鍗佸瓧宸﹁竟鐩镐箻绛変簬浜屾椤圭郴鏁帮紝鍙宠竟鐩镐箻绛変簬甯告暟椤癸紝浜ゅ弶鐩镐箻鍐嶇浉鍔犵瓑浜庝竴娆￠」绯绘暟銆傚叾瀹炲氨鏄繍鐢ㄤ箻娉曞叕寮(x+a)(x+b)=x²+(a+b)x+ab鐨勯嗚繍绠楁潵杩涜鍥犲紡鍒嗚В銆傝繍绠椾妇渚嬶細a²+a-42 棣栧厛锛岀湅鐪嬬涓涓暟锛屾槸a²锛屼唬琛ㄦ槸涓や釜a鐩镐箻寰楀埌鐨勶紝鍒欐帹鏂嚭(...
绛旓細瀵逛簬浜屾椤圭郴鏁版槸1鐨勪簩娆′笁椤瑰紡锛屼篃鍙互鐢鍗佸瓧鐩镐箻娉曞垎瑙鍥犲紡锛岃繖鏃跺彧闇鑰冭檻濡備綍鎶婂父鏁伴」鍒嗚В鍥犳暟.渚嬪鎶妜^2+2x-15鍒嗚В鍥犲紡锛屽崄瀛楃浉涔樻硶鏄 1 -3 鈺 1 5 1脳5+1脳(-3)=2 鎵浠^2+2x-15=(x-3)(x+5).渚3 鎶5x^2+6xy-8y^2鍒嗚В鍥犲紡.鍒嗘瀽锛氳繖涓椤瑰紡鍙互鐪嬩綔鏄叧浜巟鐨勪簩娆′笁椤瑰紡锛...
绛旓細浠庤屽緱鍒版渶缁堢殑鍒嗚В寮忋傞渶瑕佹敞鎰忕殑鏄紝鍗佸瓧鐩镐箻娉閫傜敤浜庝竴鍏冧簩娆″椤瑰紡鐨勫垎瑙鍥犲紡锛岃屼笖瑕佹眰澶氶」寮忕殑绯绘暟閮戒负鏁存暟銆傝繖绉嶆柟娉曞湪姹傝В澶嶆潅鎴栭珮闃跺椤瑰紡鏃舵晥鐜囪緝浣庯紝闇瑕佸熷姪鍏朵粬鏂规硶鎴栧伐鍏疯繘琛屾眰瑙ｃ傛讳箣锛屽崄瀛楃浉涔樻硶鏄竴绉嶅緢瀹炵敤鐨勫垎瑙ｅ洜寮忕殑鏂规硶锛屽湪瀛︿範澶氶」寮忥紝浠ｆ暟寮忕瓑鏁板鎶宸ф椂鍏锋湁鍗佸垎閲嶈鐨勬剰涔夈
绛旓細杩愮敤鍗佸瓧鐩镐箻娉曟妸涓涓簩娆￠」绯绘暟涓嶆槸1鐨勪簩娆′笁椤瑰紡鍥犲紡鍒嗚В锛屽線寰瑕佺粡杩囧娆¤瀵燂紝鎵嶈兘纭畾鏄惁鍙互鐢鍗佸瓧鐩镐箻娉曞垎瑙鍥犲紡. 瀵逛簬浜屾椤圭郴鏁版槸1鐨勪簩娆′笁椤瑰紡锛屼篃鍙互鐢ㄥ崄瀛楃浉涔樻硶鍒嗚В鍥犲紡锛岃繖鏃跺彧闇鑰冭檻濡備綍鎶婂父鏁伴」鍒嗚В鍥犳暟.渚嬪鎶妜^2+2x-15鍒嗚В鍥犲紡锛屽崄瀛楃浉涔樻硶鏄 1 -3 鈺 1 5 1脳5+1脳(-3)...
绛旓細鍗佸瓧鐩镐箻娉鑳芥妸鏌愪簺浜屾涓夐」寮廰x2+bx+c(a鈮0)鍒嗚В鍥犲紡銆傝繖绉嶆柟娉曠殑鍏冲仴鏄妸浜屾椤圭殑绯绘暟a鍒嗚В鎴愪袱涓洜鏁癮1,a2鐨勭Нa1•a2锛屾妸甯告暟椤筩鍒嗚В鎴愪袱涓洜鏁癱1,c2鐨勭Нc1•c2锛屽苟浣縜1c2+a2c1姝ｅソ鏄竴娆￠」绯绘暟b锛岄偅涔堝彲浠ョ洿鎺ュ啓鎴愮粨鏋滐細ax2+bx+c=(a1x+c1)(a2x+c2),鍦ㄨ繍鐢ㄨ繖绉嶆柟娉...
绛旓細浜屽厓涓娆℃柟绋鍗佸瓧鐩镐箻娉濡備笅锛氫簩鍏冧竴娆℃柟绋嬫槸涓绉嶅父瑙佺殑鏁板鏂圭▼锛屽畠鐨勫舰寮忎负 ax + b = 0锛屽叾涓璦鍜宐鏄父鏁帮紝x鏄湭鐭ユ暟銆傚浜庝竴浜涚壒瀹氱殑a鍜宐鐨勫硷紝鍙互浣跨敤鍗佸瓧鐩镐箻娉曞皢浜屽厓涓娆℃柟绋鍒嗚В鍥犲紡锛屼粠鑰屾眰鍑簒鐨勫笺傚崄瀛楃浉涔樻硶鏄竴绉嶅皢涓や釜鏁板垎瑙ｆ垚涓や釜鍥犲瓙鐨勬柟娉曪紝杩欎袱涓洜瀛愬彲浠ラ氳繃浜ゅ弶鐩镐箻寰楀埌鍘熷...
