求10道平方差公式、完全平方公式的难题 求平方差公式和完全平方公式的练习题 特难的
\u6c42\u901a\u8fc7\u201c\u5e73\u65b9\u5dee\u516c\u5f0f\u201d\u548c\u201c\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u201d\u5206\u89e3\u56e0\u5f0f\u7684\u96be\u9898\u4e00.4\uff082a+b\uff09\u7684\u5e73\u65b9-12\uff082a+b\uff09+9
\u89e3\uff1a\u539f\u5f0f=[2\uff082a+b\uff09]²-2\u00d72\u00d73\uff082a+b\uff09+3²
=[2\uff082a+b\uff09-3]²
\u4e8c.\u4e94\u5206\u4e4b\u4e00x\u7684\u5e73\u65b9y\u2014x\u7684\u56db\u6b21\u65b9\u2014 \u4e00\u767e\u5206\u4e4by\u7684\u5e73\u65b9
\u89e3\uff1a\u539f\u5f0f=-[\uff08X²\uff09²-2\u00d7X²\u00d7\uff081\uff0f10\uff09Y+\uff08Y\uff0f10\uff09]²
=-[\uff08X²\uff09+\uff08Y\uff0f10\uff09]²
\u4e09.9+6\uff08a+b\uff09+\uff08a+b\uff09\u7684\u5e73\u65b9
\u89e3\uff1a\u539f\u5f0f=3²+2\u00d73\u00d7\uff08a+b\uff09+\uff08a+b\uff09²
=[3+\uff08a+b\uff09]²
\u56db.144\u5206\u4e4bm\u7684\u5e73\u65b9\u20146\u5206\u4e4bmn+n\u7684\u5e73\u65b9
\u89e3\uff1a\u539f\u5f0f=\uff08m\uff0f12\uff09²-2\u00d7\uff081\uff0f12\uff09mn+n²
=[\uff08m\uff0f12\uff09-n]²
\u4e94.\uff08x+y\uff09\u7684\u5e73\u65b9+6\uff08x+y\uff09+9
\u89e3\uff1a\u539f\u5f0f=.\uff08x+y\uff09²+2\u00d73\uff08x+y\uff09+3²
=[\uff08x+y\uff09+3]²
\u96be\u4e5f\u96be\u4e0d\u5230\u54ea\u91cc\u53bb,\u521d\u4e00\u7684\u6570\u5b66\u59cb\u7ec8\u6709\u4e2a\u91cf.
\u96be\u7684\u548c\u7b80\u5355\u7684\u6839\u672c\u6ca1\u533a\u522b,
\u90fd\u662f\u6309\u516c\u5f0f\u8ba1\u7b97,\u6240\u4ee5\u6ca1\u6709\u7279\u96be\u7684.
\u5e73\u65b9\u5dee\u516c\u5f0f-
\u8bf4\u4e0b\u6cd5\u5219:(a+b)(a-b)=a²-b²,\u4e24\u6570\u548c\u4e0e\u8fd9\u4e24\u6570\u5dee\u7684\u79ef,\u7b49\u4e8e\u5b83\u4eec\u7684\u5e73\u65b9\u5dee.
\u7b2c\u4e00\u9053(x+2)(x-2)=x²-2²=x²-4
\u7b2c\u4e8c\u9053(1+3a)(1-3a)=1²+3a²=1+9a²
\u7b2c\u4e09\u9053(x+5y)(x-5y)=x²-5y²=x²-25y²
\u7b2c\u56db\u9053(y+3z)(y-3z)=y²-3z²=y²-9z²
\u7b2c\u4e94\u9053(5+6x)(5-6x)=5²-6x²=25-36x²
\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f-
\u5b8c\u5168\u5e73\u65b9\u516c\u5f0f\u6cd5\u5219:\u2460(a+b)²=a²+2ab+b² \u2461(a-b)²=a²-2ab+b²
\u7b2c\u4e00\u9053(2x-3)²=(2x)²-2\u00d7(2x)\u00d73+3²=4x²-12x+9
\u7b2c\u4e8c\u9053(4x+5y)²=(4x)²+2\u00d7(4x)\u00d7(5y)+(5y)²=16x²+40xy+25y²
\u7b2c\u4e09\u9053(mn-a)²=(mn)²-2\u00d7(mn)\u00d7a+a²=m²n²-2amn+a²
\u7b2c\u56db\u9053(x+3)²-x²=x²+6x+9-x²=6x+9
\u7b2c\u4e94\u9053(a+b+3)(a+b-3)=[(a+b)+3][(a+b)-3]=(a+b)²-3²=a²+2ab=b²-9
\u7b2c\u516d\u9053(\u6709\u4e2a\u89e3\u6cd5\u53ef\u4ee5\u8fd9\u6837):1007\u00d7993
=(1000+7)(1000-7)
=1000²-7²
=1000000-49
=999951
\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u91c7\u7eb3\u6211\u5427\u8c22\u8c22~~~
2若a4+b4+c4+d4=4abcd ,a,b,c,d>0,证明：a=b=c=d
3a,b为正整数，a2-b2=68,求a,b
绛旓細29,X^+27X+26 =(x+26)(x+1)30,X^+12X+20 =(x+2)(x+10)
绛旓細1銆佸畬鍏ㄥ钩鏂瑰樊鍏紡锛(a-b)²=a²-2ab+b²瀹屽叏骞虫柟宸锛氫袱鏁板樊鐨勫钩鏂癸紝绛変簬瀹冧滑鐨勫钩鏂瑰拰锛屽噺鍘诲畠浠殑绉殑2鍊嶅嵆瀹屽叏骞虫柟鍏紡銆備緥鍙ワ細(6-4)²=6²-2x6x4+4²=36-48+16=4 2銆佸钩鏂瑰樊鍏紡锛歛²-b²=(a+b)(a-b)骞虫柟宸細涓涓钩鏂规暟鎴栨鏂瑰舰锛...
绛旓細瀹屽叏骞虫柟宸叕寮忥細(a-b)2=a2-2ab+b2瀹屽叏骞虫柟宸锛氫袱鏁板樊鐨勫钩鏂癸紝绛変簬瀹冧滑鐨勫钩鏂瑰拰锛屽噺鍘诲畠浠殑'绉殑2鍊嶅嵆瀹屽叏骞虫柟鍏紡銆備緥鍙ワ細(6-4)2=62-2x6x4+42=36-48+16=4 瀹屽叏骞虫柟鍏紡骞虫柟宸叕寮忓尯鍒細璁＄畻鍏蜂綋鏁版嵁缁撴灉涓嶅悓锛堣嫢a=2锛宐=1锛夊畬鍏ㄥ钩鏂瑰樊鍏紡锛氾紙a-b锛2=a2-2ab+b2=1銆傚钩鏂瑰樊鍏紡锛歛...
绛旓細1姹傝瘉锛歛2+b2+c2>=ab+ac+bc 2鑻4+b4+c4+d4=4abcd ,a,b,c,d>0,璇佹槑锛歛=b=c=d 3a,b涓烘鏁存暟锛宎2-b2=68,姹俛,b
绛旓細10,X^-8X-48 =(x-12)(x+4)11,X^-49X+48 =(x-48)(x-1)12,X^+14X+48 =(x+6)(x+8)13,X^+34X+33 =(x+33)(x+1)14,X^+29X+100 =(x+25)(x+4)15,X^-34X+33 =(x-33)(x-1)16,X^-32X-33 =(x-33)(x+1)17,X^+3X+2 =(x+2)(x+1)18,X^+11X+28...
绛旓細(4a+3b+c)锛漑(4a+c)-3b][(4a+c)+3b]锛(4a+c)2-(3b)2 锛16a2+8ac+c2-9b2锛庢湰棰樻槸骞虫柟宸叕寮涓瀹屽叏骞虫柟鍏紡缁煎悎杩愮敤鐨勮绠楅锛庡厛杩愮敤骞虫柟宸叕寮忎氦鎹㈡垚鍚岄」鍦ㄥ墠鐩稿弽椤瑰湪鍚庝负(4a+c-3b)(4a+c+3b)锛庡啀鐢ㄥ钩鏂瑰樊鍏紡涓殑a浠ｆ崲4a+c锛宐浠ｆ崲3b锛庢渶鍚庣敤瀹屽叏骞虫柟鍏紡璁＄畻(4a+c)2锛
绛旓細瀹屽叏骞虫柟宸叓涓叕寮忚В閲婂涓嬶細1銆(a^2 - b^2 = (a+b)(a-b)):杩欎釜鍏紡琛ㄧず浜嗕袱涓暟鐨勫钩鏂瑰樊鍙互閫氳繃灏嗗畠浠浉鍔犱笌鐩稿噺鐨勪箻绉潵琛ㄧず銆傚畠鏄簩娆″樊鍏紡鐨勪竴绉嶅舰寮忋2銆((a\pm b)^2 = a^2 \pm 2ab + b^2):杩欎釜鍏紡鏄骞虫柟宸叕寮鐨勫父瑙佸舰寮忋傚畠琛ㄧず浜嗕竴涓簩娆″椤瑰紡鐨勫钩鏂瑰彲浠ラ氳繃骞虫柟...
绛旓細锛1锛夛紙3x+2锛夛紙3x-2锛夈傦紙2锛夛紙b+2a锛夛紙2a-b锛夈傚钩鏂瑰樊鍏紡 (a+b)(a-b) = a2-b2銆傚畬鍏ㄥ钩鏂瑰叕寮(a+b)2=a2+2ab+b2 (a-b)2=a2-2ab+b2銆傚畬鍏ㄥ钩鏂规敞鎰忎簨椤癸細1銆佸乏杈规槸涓涓簩椤瑰紡鐨勫畬鍏ㄥ钩鏂广2銆佸彸杈规槸浜岄」骞虫柟鐨勫拰锛屽姞涓婏紙鎴栧噺鍘伙級杩欎袱椤逛箻绉殑浜屽嶏紝a鍜宐鍙槸鏁帮紝鍗曢」寮忥紝...
绛旓細骞虫柟宸叕寮- 璇翠笅娉曞垯:(a+b)(a-b)=a²-b²,涓ゆ暟鍜屼笌杩欎袱鏁板樊鐨勭Н,绛変簬瀹冧滑鐨勫钩鏂瑰樊.绗竴閬(x+2)(x-2)=x²-2²=x²-4 绗簩閬(1+3a)(1-3a)=1²+3a²=1+9a²绗笁閬(x+5y)(x-5y)=x²-5y²=x²-25y²...
绛旓細瀹屽叏骞虫柟鍏紡锛(a+b)2 = a2 + 2ab + b2 锛坅-b)2 = a2 - 2ab + b2 骞虫柟宸叕寮锛歛2 - b2 = (a+b)(a-b)p.s.鍥犱负涓嶄細鎵撲笂鏍囷紝瀛楁瘝鍚庨潰鐨2琛ㄧず骞虫柟浜 鏈変簡鍏紡寰閲屼唬鏁颁笉灏辫浜嗗悧锛屼妇涓緥瀛愬惂锛屽鏋渂=10 (a+10)2 = a2 + 20a + 100 (a-100)2 = a2 - 20a + 100 a...
