几道初二年级的因式分解题。（要有详细的解题过程。） 一道初二因式分解的题（要过程和答案）
\u4e24\u9053\u521d\u4e8c\u6570\u5b66\u9898\uff08\u56e0\u5f0f\u5206\u89e3\uff09\u8981\u6709\u8be6\u7ec6\u89e3\u7b54\u8fc7\u7a0b\u2474\u63d0\u516c\u56e0\u5f0f\u6cd5
\u5404\u9879\u90fd\u542b\u6709\u7684\u516c\u5171\u7684\u56e0\u5f0f\u53eb\u505a\u8fd9\u4e2a\u591a\u9879\u5f0f\u5404\u9879\u7684\u516c\u56e0\u5f0f\u3002
\u5982\u679c\u4e00\u4e2a\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u53ef\u4ee5\u628a\u8fd9\u4e2a\u516c\u56e0\u5f0f\u63d0\u51fa\u6765\uff0c\u4ece\u800c\u5c06\u591a\u9879\u5f0f\u5316\u6210\u4e24\u4e2a\u56e0\u5f0f\u4e58\u79ef\u7684\u5f62\u5f0f\uff0c\u8fd9\u79cd\u5206\u89e3\u56e0\u5f0f\u7684\u65b9\u6cd5\u53eb\u505a\u63d0\u516c\u56e0\u5f0f\u6cd5\u3002
\u5177\u4f53\u65b9\u6cd5\uff1a\u5f53\u5404\u9879\u7cfb\u6570\u90fd\u662f\u6574\u6570\u65f6\uff0c\u516c\u56e0\u5f0f\u7684\u7cfb\u6570\u5e94\u53d6\u5404\u9879\u7cfb\u6570\u7684\u6700\u5927\u516c\u7ea6\u6570\uff1b\u5b57\u6bcd\u53d6\u5404\u9879\u7684\u76f8\u540c\u7684\u5b57\u6bcd\uff0c\u800c\u4e14\u5404\u5b57\u6bcd\u7684\u6307\u6570\u53d6\u6b21\u6570\u6700\u4f4e\u7684\uff1b\u53d6\u76f8\u540c\u7684\u591a\u9879\u5f0f\uff0c\u591a\u9879\u5f0f\u7684\u6b21\u6570\u53d6\u6700\u4f4e\u7684\u3002
\u5982\u679c\u591a\u9879\u5f0f\u7684\u7b2c\u4e00\u9879\u662f\u8d1f\u7684\uff0c\u4e00\u822c\u8981\u63d0\u51fa\u201c-\u201d\u53f7\uff0c\u4f7f\u62ec\u53f7\u5185\u7684\u7b2c\u4e00\u9879\u7684\u7cfb\u6570\u6210\u4e3a\u6b63\u6570\u3002\u63d0\u51fa\u201c-\u201d\u53f7\u65f6\uff0c\u591a\u9879\u5f0f\u7684\u5404\u9879\u90fd\u8981\u53d8\u53f7\u3002
\u4f8b\u5982\uff1a-am+bm+cm=-m(a-b-c)\uff1b
a(x-y)+b(y-x)=a(x-y)-b(x-y)=(x-y)(a-b)\u3002
\u6ce8\u610f\uff1a\u628a2a^2+1/2\u53d8\u62102(a^2+1/4)\u4e0d\u53eb\u63d0\u516c\u56e0\u5f0f
\u2475\u516c\u5f0f\u6cd5
\u5982\u679c\u628a\u4e58\u6cd5\u516c\u5f0f\u53cd\u8fc7\u6765\uff0c\u5c31\u53ef\u4ee5\u628a\u67d0\u4e9b\u591a\u9879\u5f0f\u5206\u89e3\u56e0\u5f0f\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u516c\u5f0f\u6cd5\u3002
\u5e73\u65b9\u5dee\u516c\u5f0f\uff1aa^2-b^2=(a+b)(a-b)\uff1b
\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\uff1aa^2\u00b12ab\uff0bb^2\uff1d(a\u00b1b)^2\uff1b
\u6ce8\u610f\uff1a\u80fd\u8fd0\u7528\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u5206\u89e3\u56e0\u5f0f\u7684\u591a\u9879\u5f0f\u5fc5\u987b\u662f\u4e09\u9879\u5f0f\uff0c\u5176\u4e2d\u6709\u4e24\u9879\u80fd\u5199\u6210\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u5e73\u65b9\u548c\u7684\u5f62\u5f0f\uff0c\u53e6\u4e00\u9879\u662f\u8fd9\u4e24\u4e2a\u6570(\u6216\u5f0f)\u7684\u79ef\u76842\u500d\u3002
\u7acb\u65b9\u548c\u516c\u5f0f\uff1aa^3+b^3=(a+b)(a^2-ab+b^2)\uff1b
\u7acb\u65b9\u5dee\u516c\u5f0f\uff1aa^3-b^3=(a-b)(a^2+ab+b^2)\uff1b
\u5b8c\u5168\u7acb\u65b9\u516c\u5f0f\uff1aa^3\u00b13a^2b\uff0b3ab^2\u00b1b^3=(a\u00b1b)^3\uff0e
\u5176\u4f59\u516c\u5f0f\u8bf7\u53c2\u770b\u4e0a\u8fb9\u7684\u56fe\u7247\u3002
\u4f8b\u5982\uff1aa^2 +4ab+4b^2 =(a+2b)^2(\u53c2\u770b\u53f3\u56fe)\uff0e
[\u7f16\u8f91\u672c\u6bb5]\u7ade\u8d5b\u7528\u5230\u7684\u65b9\u6cd5
\u2476\u5206\u7ec4\u5206\u89e3\u6cd5
\u5206\u7ec4\u5206\u89e3\u662f\u89e3\u65b9\u7a0b\u7684\u4e00\u79cd\u7b80\u6d01\u7684\u65b9\u6cd5\uff0c\u6211\u4eec\u6765\u5b66\u4e60\u8fd9\u4e2a\u77e5\u8bc6\u3002
\u80fd\u5206\u7ec4\u5206\u89e3\u7684\u65b9\u7a0b\u6709\u56db\u9879\u6216\u5927\u4e8e\u56db\u9879\uff0c\u4e00\u822c\u7684\u5206\u7ec4\u5206\u89e3\u6709\u4e24\u79cd\u5f62\u5f0f\uff1a\u4e8c\u4e8c\u5206\u6cd5\uff0c\u4e09\u4e00\u5206\u6cd5\u3002
\u6bd4\u5982\uff1a
ax+ay+bx+by
=a(x+y)+b(x+y)
=(a+b)(x+y)
\u6211\u4eec\u628aax\u548cay\u5206\u4e00\u7ec4\uff0cbx\u548cby\u5206\u4e00\u7ec4\uff0c\u5229\u7528\u4e58\u6cd5\u5206\u914d\u5f8b\uff0c\u4e24\u4e24\u76f8\u914d\uff0c\u7acb\u5373\u89e3\u9664\u4e86\u56f0\u96be\u3002
\u540c\u6837\uff0c\u8fd9\u9053\u9898\u4e5f\u53ef\u4ee5\u8fd9\u6837\u505a\u3002
ax+ay+bx+by
=x(a+b)+y(a+b)
=(a+b)(x+y)
\u51e0\u9053\u4f8b\u9898\uff1a
1. 5ax+5bx+3ay+3by
\u89e3\u6cd5\uff1a=5x(a+b)+3y(a+b)
=(5x+3y)(a+b)
\u8bf4\u660e\uff1a\u7cfb\u6570\u4e0d\u4e00\u6837\u4e00\u6837\u53ef\u4ee5\u505a\u5206\u7ec4\u5206\u89e3\uff0c\u548c\u4e0a\u9762\u4e00\u6837\uff0c\u628a5ax\u548c5bx\u770b\u6210\u6574\u4f53\uff0c\u628a3ay\u548c3by\u770b\u6210\u4e00\u4e2a\u6574\u4f53\uff0c\u5229\u7528\u4e58\u6cd5\u5206\u914d\u5f8b\u8f7b\u677e\u89e3\u51fa\u3002
2. x3-x2+x-1
\u89e3\u6cd5\uff1a=(x3-x2)+(x-1)
=x2(x-1)+(x-1)
=(x-1)(x2+1)
\u5229\u7528\u4e8c\u4e8c\u5206\u6cd5\uff0c\u63d0\u516c\u56e0\u5f0f\u6cd5\u63d0\u51fax2\uff0c\u7136\u540e\u76f8\u5408\u8f7b\u677e\u89e3\u51b3\u3002
3. x2-x-y2-y
\u89e3\u6cd5\uff1a=(x2-y2)-(x+y)
=(x+y)(x-y)-(x+y)
=(x+y)(x-y-1)
\u5229\u7528\u4e8c\u4e8c\u5206\u6cd5\uff0c\u518d\u5229\u7528\u516c\u5f0f\u6cd5a2-b2=(a+b)(a-b)\uff0c\u7136\u540e\u76f8\u5408\u89e3\u51b3\u3002
\u2477\u5341\u5b57\u76f8\u4e58\u6cd5
\u8fd9\u79cd\u65b9\u6cd5\u6709\u4e24\u79cd\u60c5\u51b5\u3002
\u2460x^2+(p+q)x+pq\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u8fd9\u7c7b\u4e8c\u6b21\u4e09\u9879\u5f0f\u7684\u7279\u70b9\u662f\uff1a\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\uff1b\u5e38\u6570\u9879\u662f\u4e24\u4e2a\u6570\u7684\u79ef\uff1b\u4e00\u6b21\u9879\u7cfb\u6570\u662f\u5e38\u6570\u9879\u7684\u4e24\u4e2a\u56e0\u6570\u7684\u548c\u3002\u56e0\u6b64\uff0c\u53ef\u4ee5\u76f4\u63a5\u5c06\u67d0\u4e9b\u4e8c\u6b21\u9879\u7684\u7cfb\u6570\u662f1\u7684\u4e8c\u6b21\u4e09\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\uff1ax^2+(p+q)x+pq=(x+p)(x+q) \uff0e
\u2461kx^2+mx+n\u578b\u7684\u5f0f\u5b50\u7684\u56e0\u5f0f\u5206\u89e3
\u5982\u679c\u5982\u679c\u6709k=ac\uff0cn=bd\uff0c\u4e14\u6709ad+bc=m\u65f6\uff0c\u90a3\u4e48kx^2+mx+n=(ax+b)(cx+d)\uff0e
\u56fe\u793a\u5982\u4e0b\uff1a
a b
\u00d7
c d
\u4f8b\u5982\uff1a\u56e0\u4e3a
1 -3
\u00d7
7 2
-3\u00d77=-21\uff0c1\u00d72=2\uff0c\u4e142-21=-19\uff0c
\u6240\u4ee57x^2-19x-6=(7x+2)(x-3)\uff0e
\u5341\u5b57\u76f8\u4e58\u6cd5\u53e3\u8bc0\uff1a\u9996\u5c3e\u5206\u89e3\uff0c\u4ea4\u53c9\u76f8\u4e58\uff0c\u6c42\u548c\u51d1\u4e2d
\u2478\u62c6\u9879\u3001\u6dfb\u9879\u6cd5
\u8fd9\u79cd\u65b9\u6cd5\u6307\u628a\u591a\u9879\u5f0f\u7684\u67d0\u4e00\u9879\u62c6\u5f00\u6216\u586b\u8865\u4e0a\u4e92\u4e3a\u76f8\u53cd\u6570\u7684\u4e24\u9879\uff08\u6216\u51e0\u9879\uff09\uff0c\u4f7f\u539f\u5f0f\u9002\u5408\u4e8e\u63d0\u516c\u56e0\u5f0f\u6cd5\u3001\u8fd0\u7528\u516c\u5f0f\u6cd5\u6216\u5206\u7ec4\u5206\u89e3\u6cd5\u8fdb\u884c\u5206\u89e3\u3002\u8981\u6ce8\u610f\uff0c\u5fc5\u987b\u5728\u4e0e\u539f\u591a\u9879\u5f0f\u76f8\u7b49\u7684\u539f\u5219\u4e0b\u8fdb\u884c\u53d8\u5f62\u3002
\u4f8b\u5982\uff1abc(b+c)+ca(c-a)-ab(a+b)
=bc(c-a+a+b)+ca(c-a)-ab(a+b)
=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)
=c(c-a)(b+a)+b(a+b)(c-a)
=(c+b)(c-a)(a+b)\uff0e
\u2479\u914d\u65b9\u6cd5
\u5bf9\u4e8e\u67d0\u4e9b\u4e0d\u80fd\u5229\u7528\u516c\u5f0f\u6cd5\u7684\u591a\u9879\u5f0f\uff0c\u53ef\u4ee5\u5c06\u5176\u914d\u6210\u4e00\u4e2a\u5b8c\u5168\u5e73\u65b9\u5f0f\uff0c\u7136\u540e\u518d\u5229\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\uff0c\u5c31\u80fd\u5c06\u5176\u56e0\u5f0f\u5206\u89e3\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u914d\u65b9\u6cd5\u3002\u5c5e\u4e8e\u62c6\u9879\u3001\u8865\u9879\u6cd5\u7684\u4e00\u79cd\u7279\u6b8a\u60c5\u51b5\u3002\u4e5f\u8981\u6ce8\u610f\u5fc5\u987b\u5728\u4e0e\u539f\u591a\u9879\u5f0f\u76f8\u7b49\u7684\u539f\u5219\u4e0b\u8fdb\u884c\u53d8\u5f62\u3002
\u4f8b\u5982\uff1ax^2+3x-40
=x^2+3x+2.25-42.25
=(x+1.5)^2-(6.5)^2
=(x+8)(x-5)\uff0e
\u247a\u5e94\u7528\u56e0\u5f0f\u5b9a\u7406
\u5bf9\u4e8e\u591a\u9879\u5f0ff(x)=0\uff0c\u5982\u679cf(a)=0\uff0c\u90a3\u4e48f(x)\u5fc5\u542b\u6709\u56e0\u5f0fx-a\uff0e
\u4f8b\u5982\uff1af(x)=x^2+5x+6\uff0cf(-2)=0\uff0c\u5219\u53ef\u786e\u5b9ax+2\u662fx^2+5x+6\u7684\u4e00\u4e2a\u56e0\u5f0f\u3002(\u4e8b\u5b9e\u4e0a\uff0cx^2+5x+6=(x+2)(x+3)\uff0e)
\u247b\u6362\u5143\u6cd5
\u6709\u65f6\u5728\u5206\u89e3\u56e0\u5f0f\u65f6\uff0c\u53ef\u4ee5\u9009\u62e9\u591a\u9879\u5f0f\u4e2d\u7684\u76f8\u540c\u7684\u90e8\u5206\u6362\u6210\u53e6\u4e00\u4e2a\u672a\u77e5\u6570\uff0c\u7136\u540e\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\uff0c\u6700\u540e\u518d\u8f6c\u6362\u56de\u6765\uff0c\u8fd9\u79cd\u65b9\u6cd5\u53eb\u505a\u6362\u5143\u6cd5\u3002
\u6ce8\u610f:\u6362\u5143\u540e\u52ff\u5fd8\u8fd8\u5143.
\u4f8b\u5982\u5728\u5206\u89e3(x^2+x+1)(x^2+x+2)-12\u65f6\uff0c\u53ef\u4ee5\u4ee4y=x^2+x,\u5219
\u539f\u5f0f=(y+1)(y+2)-12
=y^2+3y+2-12=y^2+3y-10
=(y+5)(y-2)
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)\uff0e
\u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002
\u247c\u6c42\u6839\u6cd5
\u4ee4\u591a\u9879\u5f0ff(x)=0,\u6c42\u51fa\u5176\u6839\u4e3ax1\uff0cx2\uff0cx3\uff0c\u2026\u2026xn\uff0c\u5219\u8be5\u591a\u9879\u5f0f\u53ef\u5206\u89e3\u4e3af(x)=(x-x1)(x-x2)(x-x3)\u2026\u2026(x-xn) \uff0e
\u4f8b\u5982\u5728\u5206\u89e32x^4+7x^3-2x^2-13x+6\u65f6\uff0c\u4ee42x^4 +7x^3-2x^2-13x+6=0\uff0c
\u5219\u901a\u8fc7\u7efc\u5408\u9664\u6cd5\u53ef\u77e5\uff0c\u8be5\u65b9\u7a0b\u7684\u6839\u4e3a0.5 \uff0c-3\uff0c-2\uff0c1\uff0e
\u6240\u4ee52x^4+7x^3-2x^2-13x+6=(2x-1)(x+3)(x+2)(x-1)\uff0e
\u247d\u56fe\u8c61\u6cd5
\u4ee4y=f(x)\uff0c\u505a\u51fa\u51fd\u6570y=f(x)\u7684\u56fe\u8c61\uff0c\u627e\u5230\u51fd\u6570\u56fe\u50cf\u4e0eX\u8f74\u7684\u4ea4\u70b9x1 ,x2 ,x3 ,\u2026\u2026xn \uff0c\u5219\u591a\u9879\u5f0f\u53ef\u56e0\u5f0f\u5206\u89e3\u4e3af(x)= f(x)=(x-x1)(x-x2)(x-x3)\u2026\u2026(x-xn)\uff0e
\u4e0e\u65b9\u6cd5\u247c\u76f8\u6bd4\uff0c\u80fd\u907f\u5f00\u89e3\u65b9\u7a0b\u7684\u7e41\u7410\uff0c\u4f46\u662f\u4e0d\u591f\u51c6\u786e\u3002
\u4f8b\u5982\u5728\u5206\u89e3x^3 +2x^2 -5x-6\u65f6\uff0c\u53ef\u4ee5\u4ee4y=x^3 +2x^2 -5x-6.
\u4f5c\u51fa\u5176\u56fe\u50cf\uff0c\u4e0ex\u8f74\u4ea4\u70b9\u4e3a-3\uff0c-1\uff0c2
\u5219x^3 +2x^2-5x-6=(x+1)(x+3)(x-2)\uff0e
\u247e\u4e3b\u5143\u6cd5
\u5148\u9009\u5b9a\u4e00\u4e2a\u5b57\u6bcd\u4e3a\u4e3b\u5143\uff0c\u7136\u540e\u628a\u5404\u9879\u6309\u8fd9\u4e2a\u5b57\u6bcd\u6b21\u6570\u4ece\u9ad8\u5230\u4f4e\u6392\u5217\uff0c\u518d\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u247f\u7279\u6b8a\u503c\u6cd5
\u5c062\u621610\u4ee3\u5165x\uff0c\u6c42\u51fa\u6570p\uff0c\u5c06\u6570p\u5206\u89e3\u8d28\u56e0\u6570\uff0c\u5c06\u8d28\u56e0\u6570\u9002\u5f53\u7684\u7ec4\u5408\uff0c\u5e76\u5c06\u7ec4\u5408\u540e\u7684\u6bcf\u4e00\u4e2a\u56e0\u6570\u5199\u62102\u621610\u7684\u548c\u4e0e\u5dee\u7684\u5f62\u5f0f\uff0c\u5c062\u621610\u8fd8\u539f\u6210x\uff0c\u5373\u5f97\u56e0\u5f0f\u5206\u89e3\u5f0f\u3002
\u4f8b\u5982\u5728\u5206\u89e3x^3+9x^2+23x+15\u65f6\uff0c\u4ee4x=2\uff0c\u5219
x^3 +9x^2 +23x+15=8+36+46+15=105\uff0c
\u5c06105\u5206\u89e3\u62103\u4e2a\u8d28\u56e0\u6570\u7684\u79ef\uff0c\u5373105=3\u00d75\u00d77 \uff0e
\u6ce8\u610f\u5230\u591a\u9879\u5f0f\u4e2d\u6700\u9ad8\u9879\u7684\u7cfb\u6570\u4e3a1\uff0c\u800c3\u30015\u30017\u5206\u522b\u4e3ax+1\uff0cx+3\uff0cx+5\uff0c\u5728x=2\u65f6\u7684\u503c\uff0c
\u5219x^3+9x^2+23x+15\u53ef\u80fd\u7b49\u4e8e(x+1)(x+3)(x+5)\uff0c\u9a8c\u8bc1\u540e\u7684\u786e\u5982\u6b64\u3002
\u2480\u5f85\u5b9a\u7cfb\u6570\u6cd5
\u9996\u5148\u5224\u65ad\u51fa\u5206\u89e3\u56e0\u5f0f\u7684\u5f62\u5f0f\uff0c\u7136\u540e\u8bbe\u51fa\u76f8\u5e94\u6574\u5f0f\u7684\u5b57\u6bcd\u7cfb\u6570\uff0c\u6c42\u51fa\u5b57\u6bcd\u7cfb\u6570\uff0c\u4ece\u800c\u628a\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u3002
\u4f8b\u5982\u5728\u5206\u89e3x^4-x^3-5x^2-6x-4\u65f6\uff0c\u7531\u5206\u6790\u53ef\u77e5\uff1a\u8fd9\u4e2a\u591a\u9879\u5f0f\u6ca1\u6709\u4e00\u6b21\u56e0\u5f0f\uff0c\u56e0\u800c\u53ea\u80fd\u5206\u89e3\u4e3a\u4e24\u4e2a\u4e8c\u6b21\u56e0\u5f0f\u3002
\u4e8e\u662f\u8bbex^4-x^3-5x^2-6x-4=(x^2+ax+b)(x^2+cx+d)
=x^4+(a+c)x^3+(ac+b+d)x^2+(ad+bc)x+bd
\u7531\u6b64\u53ef\u5f97a+c=-1\uff0c
ac+b+d=-5\uff0c
ad+bc=-6\uff0c
bd=-4\uff0e
\u89e3\u5f97a=1\uff0cb=1\uff0cc=-2\uff0cd=-4\uff0e
\u5219x^4-x^3-5x^2-6x-4=(x^2+x+1)(x^2-2x-4)\uff0e
\u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002
\u2481\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5
\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u5c5e\u4e8e\u56e0\u5f0f\u5206\u89e3\u7684\u4e00\u7c7b\uff0c\u7c7b\u4f3c\u4e8e\u5341\u5b57\u76f8\u4e58\u6cd5\u3002\u7528\u4e00\u9053\u4f8b\u9898\u6765\u8bf4\u660e\u5982\u4f55\u4f7f\u7528\u3002
\u4f8b\uff1a\u5206\u89e3\u56e0\u5f0f\uff1ax^2+5xy+6y^2+8x+18y+12\uff0e
\u5206\u6790\uff1a\u8fd9\u662f\u4e00\u4e2a\u4e8c\u6b21\u516d\u9879\u5f0f\uff0c\u53ef\u8003\u8651\u4f7f\u7528\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u89e3\uff1a
x 2y 2
\u2460 \u2461 \u2462
x 3y 6
\u2234\u539f\u5f0f=(x+2y+2)(x+3y+6)\uff0e
\u53cc\u5341\u5b57\u76f8\u4e58\u6cd5\u5176\u6b65\u9aa4\u4e3a\uff1a
\u2460\u5148\u7528\u5341\u5b57\u76f8\u4e58\u6cd5\u5206\u89e32\u6b21\u9879\uff0c\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2460\u4e2dX^2+5xy+6y^2=(x+2y)(x+3y)\uff1b
\u2461\u5148\u4f9d\u4e00\u4e2a\u5b57\u6bcd\uff08\u5982y\uff09\u7684\u4e00\u6b21\u7cfb\u6570\u5206\u6570\u5e38\u6570\u9879\u3002\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2461\u4e2d6y^2+18y+12=(2y+2)(3y+6)\uff1b
\u2462\u518d\u6309\u53e6\u4e00\u4e2a\u5b57\u6bcd\uff08\u5982x\uff09\u7684\u4e00\u6b21\u7cfb\u6570\u8fdb\u884c\u68c0\u9a8c\uff0c\u5982\u5341\u5b57\u76f8\u4e58\u56fe\u2462\uff0c\u8fd9\u4e00\u6b65\u4e0d\u80fd\u7701\uff0c\u5426\u5219\u5bb9\u6613\u51fa\u9519\u3002
[\u7f16\u8f91\u672c\u6bb5]\u591a\u9879\u5f0f\u56e0\u5f0f\u5206\u89e3\u7684\u4e00\u822c\u6b65\u9aa4\uff1a
\u2460\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5148\u63d0\u516c\u56e0\u5f0f\uff1b
\u2461\u5982\u679c\u5404\u9879\u6ca1\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u53ef\u5c1d\u8bd5\u8fd0\u7528\u516c\u5f0f\u3001\u5341\u5b57\u76f8\u4e58\u6cd5\u6765\u5206\u89e3\uff1b
\u2462\u5982\u679c\u7528\u4e0a\u8ff0\u65b9\u6cd5\u4e0d\u80fd\u5206\u89e3\uff0c\u90a3\u4e48\u53ef\u4ee5\u5c1d\u8bd5\u7528\u5206\u7ec4\u3001\u62c6\u9879\u3001\u8865\u9879\u6cd5\u6765\u5206\u89e3\uff1b
\u2463\u5206\u89e3\u56e0\u5f0f\uff0c\u5fc5\u987b\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002
\u4e5f\u53ef\u4ee5\u7528\u4e00\u53e5\u8bdd\u6765\u6982\u62ec\uff1a\u201c\u5148\u770b\u6709\u65e0\u516c\u56e0\u5f0f\uff0c\u518d\u770b\u80fd\u5426\u5957\u516c\u5f0f\u3002\u5341\u5b57\u76f8\u4e58\u8bd5\u4e00\u8bd5\uff0c\u5206\u7ec4\u5206\u89e3\u8981\u5408\u9002\u3002\u201d
\u51e0\u9053\u4f8b\u9898
1\uff0e\u5206\u89e3\u56e0\u5f0f(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2\uff0e
\u89e3\uff1a\u539f\u5f0f=(1+y)^2+2(1+y)x^2(1-y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)\uff08\u8865\u9879\uff09
=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)\uff08\u5b8c\u5168\u5e73\u65b9\uff09
=[(1+y)+x^2(1-y)]^2-(2x)^2
=[(1+y)+x^2(1-y)+2x][(1+y)+x^2(1-y)-2x]
=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)
=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]
=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)\uff0e
2\uff0e\u6c42\u8bc1\uff1a\u5bf9\u4e8e\u4efb\u4f55\u5b9e\u6570x,y\uff0c\u4e0b\u5f0f\u7684\u503c\u90fd\u4e0d\u4f1a\u4e3a33\uff1a
x^5+3x^4y-5x^3y^2-15x^2y^3+4xy^4+12y^5\uff0e
\u89e3\uff1a\u539f\u5f0f=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5)
=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)
=(x+3y)(x^4-5x^2y^2+4y^4)
=(x+3y)(x^2-4y^2)(x^2-y^2)
=(x+3y)(x+y)(x-y)(x+2y)(x-2y)\uff0e
\uff08\u5206\u89e3\u56e0\u5f0f\u7684\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u53c2\u770b\u53f3\u56fe\u3002\uff09
\u5f53y=0\u65f6\uff0c\u539f\u5f0f=x^5\u4e0d\u7b49\u4e8e33\uff1b\u5f53y\u4e0d\u7b49\u4e8e0\u65f6\uff0cx+3y\uff0cx+y\uff0cx-y\uff0cx+2y\uff0cx-2y\u4e92\u4e0d\u76f8\u540c\uff0c\u800c33\u4e0d\u80fd\u5206\u6210\u56db\u4e2a\u4ee5\u4e0a\u4e0d\u540c\u56e0\u6570\u7684\u79ef\uff0c\u6240\u4ee5\u539f\u547d\u9898\u6210\u7acb\u3002
3.\uff0e\u25b3ABC\u7684\u4e09\u8fb9a\u3001b\u3001c\u6709\u5982\u4e0b\u5173\u7cfb\u5f0f\uff1a-c^2+a^2+2ab-2bc=0\uff0c\u6c42\u8bc1\uff1a\u8fd9\u4e2a\u4e09\u89d2\u5f62\u662f\u7b49\u8170\u4e09\u89d2\u5f62\u3002
\u5206\u6790\uff1a\u6b64\u9898\u5b9e\u8d28\u4e0a\u662f\u5bf9\u5173\u7cfb\u5f0f\u7684\u7b49\u53f7\u5de6\u8fb9\u7684\u591a\u9879\u5f0f\u8fdb\u884c\u56e0\u5f0f\u5206\u89e3\u3002
\u8bc1\u660e\uff1a\u2235-c^2+a^2+2ab-2bc=0\uff0c
\u2234(a+c)(a-c)+2b(a-c)=0\uff0e
\u2234(a-c)(a+2b+c)=0\uff0e
\u2235a\u3001b\u3001c\u662f\u25b3ABC\u7684\u4e09\u6761\u8fb9\uff0c
\u2234a\uff0b2b\uff0bc\uff1e0\uff0e
\u2234a\uff0dc\uff1d0\uff0c
\u5373a\uff1dc\uff0c\u25b3ABC\u4e3a\u7b49\u8170\u4e09\u89d2\u5f62\u3002
4\uff0e\u628a-12x^2n\u00d7y^n+18x^(n+2)y^(n+1)-6x^n\u00d7y^(n-1)\u5206\u89e3\u56e0\u5f0f\u3002
\u89e3\uff1a-12x^2n\u00d7y^n+18x^(n+2)y^(n+1)-6x^n\u00d7y^(n-1)
=-6x^n\u00d7y^(n-1)(2x^n\u00d7y-3x^2y^2+1)\uff0e
[\u7f16\u8f91\u672c\u6bb5]\u56e0\u5f0f\u5206\u89e3\u56db\u4e2a\u6ce8\u610f\uff1a
\u56e0\u5f0f\u5206\u89e3\u4e2d\u7684\u56db\u4e2a\u6ce8\u610f\uff0c\u53ef\u7528\u56db\u53e5\u8bdd\u6982\u62ec\u5982\u4e0b\uff1a\u9996\u9879\u6709\u8d1f\u5e38\u63d0\u8d1f\uff0c\u5404\u9879\u6709\u201c\u516c\u201d\u5148\u63d0\u201c\u516c\u201d\uff0c\u67d0\u9879\u63d0\u51fa\u83ab\u6f0f1\uff0c\u62ec\u53f7\u91cc\u9762\u5206\u5230\u201c\u5e95\u201d\u3002 \u73b0\u4e3e\u4e0b\u4f8b \u53ef\u4f9b\u53c2\u8003
\u4f8b1 \u628a\uff0da2\uff0db2\uff0b2ab\uff0b4\u5206\u89e3\u56e0\u5f0f\u3002
\u89e3\uff1a\uff0da2\uff0db2\uff0b2ab\uff0b4\uff1d\uff0d\uff08a2\uff0d2ab\uff0bb2\uff0d4\uff09\uff1d\uff0d\uff08a\uff0db\uff0b2\uff09\uff08a\uff0db\uff0d2\uff09
\u8fd9\u91cc\u7684\u201c\u8d1f\u201d\uff0c\u6307\u201c\u8d1f\u53f7\u201d\u3002\u5982\u679c\u591a\u9879\u5f0f\u7684\u7b2c\u4e00\u9879\u662f\u8d1f\u7684\uff0c\u4e00\u822c\u8981\u63d0\u51fa\u8d1f\u53f7\uff0c\u4f7f\u62ec\u53f7\u5185\u7b2c\u4e00\u9879\u7cfb\u6570\u662f\u6b63\u7684\u3002\u9632\u6b62\u5b66\u751f\u51fa\u73b0\u8bf8\u5982\uff0d9x2\uff0b4y2\uff1d\uff08\uff0d3x\uff092\uff0d\uff082y\uff092\uff1d\uff08\uff0d3x\uff0b2y\uff09\uff08\uff0d3x\uff0d2y\uff09\uff1d\uff083x\uff0d2y\uff09\uff083x\uff0b2y\uff09\u7684\u9519\u8bef
\u4f8b2\u628a\uff0d12x2nyn\uff0b18xn\uff0b2yn\uff0b1\uff0d6xnyn\uff0d1\u5206\u89e3\u56e0\u5f0f\u3002\u89e3\uff1a\uff0d12x2nyn\uff0b18xn\uff0b2yn\uff0b1\uff0d6xnyn\uff0d1\uff1d\uff0d6xnyn\uff0d1\uff082xny\uff0d3x2y2\uff0b1\uff09
\u8fd9\u91cc\u7684\u201c\u516c\u201d\u6307\u201c\u516c\u56e0\u5f0f\u201d\u3002\u5982\u679c\u591a\u9879\u5f0f\u7684\u5404\u9879\u542b\u6709\u516c\u56e0\u5f0f\uff0c\u90a3\u4e48\u5148\u63d0\u53d6\u8fd9\u4e2a\u516c\u56e0\u5f0f\uff0c\u518d\u8fdb\u4e00\u6b65\u5206\u89e3\u56e0\u5f0f\uff1b\u8fd9\u91cc\u7684\u201c1\u201d\uff0c\u662f\u6307\u591a\u9879\u5f0f\u7684\u67d0\u4e2a\u6574\u9879\u662f\u516c\u56e0\u5f0f\u65f6\uff0c\u5148\u63d0\u51fa\u8fd9\u4e2a\u516c\u56e0\u5f0f\u540e\uff0c\u62ec\u53f7\u5185\u5207\u52ff\u6f0f\u63891\u3002
\u5206\u89e3\u56e0\u5f0f\uff0c\u5fc5\u987b\u8fdb\u884c\u5230\u6bcf\u4e00\u4e2a\u591a\u9879\u5f0f\u56e0\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u4e3a\u6b62\u3002\u5373\u5206\u89e3\u5230\u5e95\uff0c\u4e0d\u80fd\u534a\u9014\u800c\u5e9f\u7684\u610f\u601d\u3002\u5176\u4e2d\u5305\u542b\u63d0\u516c\u56e0\u5f0f\u8981\u4e00\u6b21\u6027\u63d0\u201c\u5e72\u51c0\u201d\uff0c\u4e0d\u7559\u201c\u5c3e\u5df4\u201d\uff0c\u5e76\u4f7f\u6bcf\u4e00\u4e2a\u62ec\u53f7\u5185\u7684\u591a\u9879\u5f0f\u90fd\u4e0d\u80fd\u518d\u5206\u89e3\u3002\u9632\u6b62\u5b66\u751f\u51fa\u73b0\u8bf8\u59824x4y2\uff0d5x2y2\uff0d9y2\uff1dy2\uff084x4\uff0d5x2\uff0d9\uff09\uff1dy2\uff08x2\uff0b1\uff09\uff084x2\uff0d9\uff09\u7684\u9519\u8bef\u3002
\u8003\u8bd5\u65f6\u5e94\u6ce8\u610f\uff1a
\u5728\u6ca1\u6709\u8bf4\u660e\u5316\u5230\u5b9e\u6570\u65f6\uff0c\u4e00\u822c\u53ea\u5316\u5230\u6709\u7406\u6570\u5c31\u591f\u4e86
\u7531\u6b64\u770b\u6765\uff0c\u56e0\u5f0f\u5206\u89e3\u4e2d\u7684\u56db\u4e2a\u6ce8\u610f\u8d2f\u7a7f\u4e8e\u56e0\u5f0f\u5206\u89e3\u7684\u56db\u79cd\u57fa\u672c\u65b9\u6cd5\u4e4b\u4e2d\uff0c\u4e0e\u56e0\u5f0f\u5206\u89e3\u7684\u56db\u4e2a\u6b65\u9aa4\u6216\u8bf4\u4e00\u822c\u601d\u8003\u987a\u5e8f\u7684\u56db\u53e5\u8bdd\uff1a\u201c\u5148\u770b\u6709\u65e0\u516c\u56e0\u5f0f\uff0c\u518d\u770b\u80fd\u5426\u5957\u516c\u5f0f\uff0c\u5341\u5b57\u76f8\u4e58\u8bd5\u4e00\u8bd5\uff0c\u5206\u7ec4\u5206\u89e3\u8981\u5408\u9002\u201d\u662f\u4e00\u8109\u76f8\u627f\u7684\u3002
\uff08a+x\uff09(m+1) *\uff08b+x\uff09(n-1) \u2014\uff08a+x\uff09m *\uff08b+x\uff09n
\uff08a+x\uff09
= ------------ *\uff08a+x\uff09m *\uff08b+x\uff09n \u2014\uff08a+x\uff09m *\uff08b+x\uff09n
\uff08b+x\uff09
a+x
=(------------ \u2014 1) *\uff08a+x\uff09m *\uff08b+x\uff09n
b+x
a+x b+x
= (------------ \u2014 -----------)*\uff08a+x\uff09m *\uff08b+x\uff09n
b+x b+x
a - b
= (------------)*\uff08a+x\uff09m *\uff08b+x\uff09n
b+x
= (a - b)*\uff08a+x\uff09m *\uff08b+x\uff09(n-1)
=(x-1)(x-6)(x-3)(x-4)+10
=(x2-7x+6)(x2-7x+12)+10
=(x2-7x)^2+18(x2-7x)+82
=(x2-7x)^2+18(x2-7x)+81+1
=(x2-7x+9)^2+1>0
2.x^2+4xy+4y^2-4x-8y+3
=(x+y)^2-4(x-y)+3
=(x+y-1)(x+y-3)
3.①12=3*4=1*12=2*6
所以分解的情况可能为
(a-3)(a-4)=a^2-7x+12 此时b=-7
(a-1)(a-12)=a^2-13x+12 此时b=-13
(a-2)(a-6)=a^2-8x+12 此时b=-8
②12=1+11=2+10=3+9=4+8=5+7=6+6
(a+1)(a+11)=a^2+12x+11 此时b=11
(a+2)(a+10)=a^2+12x+20 此时b=20
后面几个自己写吧
4.设一个奇数为2n+1,另一个为2n-1（n为自然数）
（2n+1)^2-(2n-1)^2
= (4n^2+4n+1)-(4n^2-4n+1)
=8n
由此可知两个相邻的奇数的平方差为8的倍数
4.设一个奇数为2x+1,另一个为2x-1（x为整数）
（2x+1)^2-(2x-1)^2
= (4x^2+4x+1)-(4x^2-4x+1)
=8x
由此可知两个相邻的奇数的平方差为8的倍数。
x^2+4xy+4y^2-4x-8y+3
=(x+2y)^2-2(2x+4y)+3
绛旓細50銆24a^3b^2梅3ab^2=8a^2,9,鍥犲紡鍒嗚В3a3b2c锛6a2b2c2锛9ab2c3锛3ab^2 c(a^2-2ac+3c^2)3.鍥犲紡鍒嗚Вxy锛6锛2x锛3y锛(x-3)(y-2)4.鍥犲紡鍒嗚Вx2(x锛峺)锛媦2(y锛峹)锛(x+y)(x-y)^2 5.鍥犲紡鍒嗚В2x2锛(a锛2b)x锛峚b锛(2x-a)(x+b)6.鍥犲紡鍒嗚Вa4锛9a2b2锛漚^2(a+3b)...
绛旓細1銆5ax+5bx+3ay+3by 瑙ｏ細=5x(a+b)+3y(a+b)=(5x+3y)(a+b)2銆亁^3-x^2+x-1 瑙ｏ細=(x^3-x^2)+(x-1)=x^2(x-1)+ (x-1)=(x-1)(x^2+1)3銆亁2-x-y2-y 瑙ｏ細=(x2-y2)-(x+y)=(x+y)(x-y)-(x+y)=(x+y)(x-y-1)4銆乥c(b+c)+ca(c-a)-ab(a+...
绛旓細1.(3a锛峛)2锛4(3a锛峛)(a锛3b)锛4(a锛3b)2锛漑3a-b-2(a+3b)]^2=(a-7b)^2 2.(a锛3)2锛6(a锛3)锛(a+3)(a-3)3(x锛1)2(x锛2)锛(x锛1)(x锛2)2锛-(x+1)(x+2)4.abc锛媋b锛4a锛漚(bc+b-4)5.16x2锛81锛(4x+9)(4x-9)6.9x2锛30x锛25锛(3x-5)^2 7....
绛旓細2. 宸茬煡A+B=8锛屼笖A²-B²=18锛屽垯浠ｆ暟寮廇-2B=-5/8 3. 宸茬煡涓姝ｆ柟褰㈢殑闈㈢Н涓9蟺X²+6蟺X+蟺锛圶锛0锛夛紝鐜板湪瑕佺敾涓涓笌姝ゆ鏂瑰舰闈㈢Н鐩哥瓑鐨勫渾锛屽垯鍦嗙殑鍗婂緞搴斾负蟺(3x+1)/2 4. 3锛圓+B锛²-27C²=3(A+B-3C)(A+B+3C)5. 1-8锛圡-N...
绛旓細2.x²锛20x锛100锛 3.x²锛4x锛3锛 4.4x²锛12x锛5锛 5.3ax²锛6ax锛 6.x(x锛2)锛峹锛 7.x²锛4x锛峚x锛4a锛 8.25x²锛49锛 9.36x²锛60x锛25锛 10.4x²锛12x锛9锛 11.x²锛9x锛18锛 12.2x²锛5x锛3锛 13.12x...
绛旓細(x-1)绗洓閬 (x+y)鐨勫钩鏂 - 4(x+y-1)=x^2-4x+y^2-4y+2xy+4 =(x+y+2)^2 绗簲閬 4(1+2x-3y) + (3y-2x)鐨勫钩鏂 =4+8x-12y+9y^2+4x^2-12xy =锛2x-3y+2锛塣2 绗叚閬 (x鐨勫洓娆℃柟 + 1)鐨勫钩鏂-(2x鐨勫钩鏂)鐨勫钩鏂 =锛坸2+1锛塣2锛坸+1锛塣2锛坸-1锛塣2 ...
绛旓細1.(x+y)²-4锛坸+y-1)=(x+y)²-4(x+y)+4 =(x+y)²-2脳2(x+y)+2²=(x+y-2)²2.(x-y)²+4xy =x²-2xy+y²+4xy =x²+2xy+y²=(x+y)²3.(x-1)(x+3)+1 =x²+2x+1-3 =(x+1)²-3...
绛旓細3.鍥犲紡鍒嗚Вxy锛6锛2x锛3y锛(x-3)(y-2)4.鍥犲紡鍒嗚Вx2(x锛峺)锛媦2(y锛峹)锛(x+y)(x-y)^2 5.鍥犲紡鍒嗚В2x2锛(a锛2b)x锛峚b锛(2x-a)(x+b)6.鍥犲紡鍒嗚Вa4锛9a2b2锛漚^2(a+3b)(a-3b)7.鑻ュ凡鐭3锛3x2锛4鍚湁x锛1鐨勫洜寮锛岃瘯鍒嗚Вx3锛3x2锛4锛(x-1)(x+2)^2 8.鍥犲紡鍒嗚Вab(...
绛旓細=2xy(6x-3y+4x²y²)3銆9y²-4x²=(3y)²-(2x)²=(3y+2x)(3y-2x)4銆4x²-4xy-9+y²=(4x²-4xy+y²)-9 =(2x-y)²-3²=(2x-y+3)(2x-y-3)寰堥珮鍏翠负鎮ㄨВ绛旓紝绁濅綘瀛︿範杩涙锛併愬涔犲疂鍏搞戝洟闃熶负鎮ㄧ瓟棰樸傛湁涓...
绛旓細(1)25a-5a^2 (2)(x-y)^2+4xy(3)x^3-3x^2y+2xy^2(4)1/2x^2-2x+2 (5)x^2-2x-3(6)a^4-2a^2b^2+b^4 (7)(x+y)(x-y-14)+49 (8) 锛坅+2b锛²锛2锛坅+2b锛+1 (9) 2a^2+2b^2+3c^2+5ab-5bc-7ac (10)x^3-6x^2+3x+10 (11) (2x+1)(...
