平方差公式计算题 平方差公式的题20道
\u5e73\u65b9\u5dee\u516c\u5f0f\u8ba1\u7b97\u9898\u3002\u89e3\uff1a\uff081\uff09-194/5x201/5
=-194x201/5x5
=-38944/25
=1599.76
\uff082\uff09 201305^5-201304x201306
=201305^5-(201305-1)(201305+1)
=201305^5-201305^2+1
=201305^3+1
\u5e0c\u671b\u5bf9\u4f60\u6709\u5e2e\u52a9\u3002
1\u3001\u8ba1\u7b97\uff1a\uff082+3x\uff09\uff08\uff0d2+3x\uff09=__________\uff1b\uff08\uff0da\uff0db\uff092=__________. 2\u3001\u4e00\u4e2a\u591a\u9879\u5f0f\u9664\u4ee5a2\uff0d6b2\u5f975a2+b2\uff0c\u90a3\u4e48\u8fd9\u4e2a\u591a\u9879\u5f0f\u662f_______________. 3\u3001\u82e5ax2+bx+c=\uff082x\uff0d1\uff09\uff08x\uff0d2\uff09\uff0c\u5219a=_____\uff0cb=_____\uff0cc=______. 4\u3001\u5df2\u77e5 (x\uff0day) (x + ay ) = x2\uff0d16y2, \u90a3\u4e48 a = __________. 5\u3001\u591a\u9879\u5f0f9x2+1\u52a0\u4e0a\u4e00\u4e2a\u5355\u9879\u5f0f\u540e\uff0c\u4f7f\u5b83\u80fd\u6210\u4e3a\u4e00\u4e2a\u6574\u5f0f\u7684\u5b8c\u5168\u5e73\u65b9\uff0c\u90a3\u4e48\u52a0\u4e0a\u7684\u5355\u9879\u5f0f\u53ef\u4ee5\u662f____________.\uff08\u586b\u4e0a\u4e00\u4e2a\u4f60\u8ba4\u4e3a\u6b63\u786e\u7684\u5373\u53ef\uff09 6\u3001\u8ba1\u7b97\uff1a\uff08a\uff0d1\uff09\uff08a+1\uff09\uff08a2\uff0d1\uff09=________. 7\u3001\u5df2\u77e5x\uff0dy=3\uff0cx2\uff0dy2=6\uff0c\u5219x+y=______. 8\u3001\u82e5x+y=5\uff0cxy=6\uff0c\u5219x2+y2=__________. 9\u3001\u5229\u7528\u4e58\u6cd5\u516c\u5f0f\u8ba1\u7b97\uff1a1012=___________;1232\uff0d124\u00d7122=____________. 10\u3001\u82e5A=\uff082\uff0d1\uff09\uff082\uff0b1\uff09\uff0822\uff0b1\uff09\uff0824\uff0b1\uff09\u2026\u2026\uff08232\uff0b1\uff09+1\uff0c\u5219A\u7684\u4e2a\u4f4d\u6570\u5b57\u662f_______. \u4e8c\u3001\u7cbe\u5fc3\u9009\u4e00\u9009\uff08\u6bcf\u5c0f\u98983\u5206\uff0c\u517130\u5206\uff09 1\u3001\u8ba1\u7b97\u7ed3\u679c\u662f2x2\uff0dx\uff0d3\u7684\u662f\uff08 \uff09 A.\uff082x\uff0d3\uff09\uff08x+1\uff09 B.\uff082x\uff0d1\uff09\uff08x\uff0d3\uff09 C.\uff082x+3\uff09\uff08x\uff0d1\uff09 D.\uff082x\uff0d1\uff09\uff08x+3\uff09 2\u3001\u4e0b\u5217\u5404\u5f0f\u7684\u8ba1\u7b97\u4e2d\uff0c\u6b63\u786e\u7684\u662f( ) A.\uff08a+5\uff09\uff08a\uff0d5\uff09=a2\uff0d5 B.\uff083x+2\uff09\uff083x\uff0d2\uff09=3x2\uff0d4 C.\uff08a+2\uff09\uff08a\uff0d3\uff09=a2\uff0d6 D.\uff083xy+1\uff09\uff083xy\uff0d1\uff09=9x2y2\uff0d1 3\u3001\u8ba1\u7b97\uff08\uff0da+2b\uff092\u7ed3\u679c\u662f\uff08 \uff09 A.\uff0da2+4ab+b2 B. a2\uff0d4ab+4b2 C.\uff0da2\uff0d4ab+b2 D. a2\uff0d2ab+2b2 4\u3001\u8bbex+y=6\uff0cx\uff0dy=5\uff0c\u5219x2\uff0dy2\u7b49\u4e8e\uff08 \uff09 A.11 B.15 C. 30 D. 60 5\u3001\u5982\u679c\uff08y+a\uff092=y2\uff0d8y+b\uff0c\u90a3\u4e48a\u3001b\u7684\u503c\u5206\u522b\u4e3a\uff08 \uff09 A. a=4\uff0cb=16 B. a=\uff0d4\uff0cb=\uff0d16 C. a=4\uff0cb=\uff0d16 D. a=\uff0d4\uff0cb=16 6\u3001\u82e5\uff08x\uff0d2y\uff092=\uff08x+2y\uff092+m,\u5219m\u7b49\u4e8e( ) A.4xy B.\uff0d4xy C. 8xy D.\uff0d8xy 7\u3001\u4e0b\u5217\u5f0f\u5b50\u53ef\u7528\u5e73\u65b9\u5dee\u516c\u5f0f\u8ba1\u7b97\u7684\u5f0f\u5b50\u662f\uff08 \uff09 A.\uff08a\uff0db\uff09\uff08b\uff0da\uff09 B.\uff08\uff0dx+1\uff09\uff08x\uff0d1\uff09 C.\uff08\uff0da\uff0db\uff09\uff08\uff0da+b\uff09 D.\uff08\uff0dx\uff0d1\uff09\uff08x+1\uff09 8\u3001\u5f53a=\uff0d1\u65f6,\u4ee3\u6570\u5f0f(a+1)2+a(a\uff0d3)\u7684\u503c\u7b49\u4e8e( ) A.\uff0d4 B. 4 C.\uff0d2 D. 2 9\u3001\u4e24\u4e2a\u8fde\u7eed\u5947\u6570\u7684\u5e73\u65b9\u5dee\u662f\uff08 \uff09 A.6\u7684\u500d\u6570 B.8\u7684\u500d\u6570 C.12\u7684\u500d\u6570 D. 16\u7684\u500d\u6570 10\u3001\u5c06\u6b63\u65b9\u5f62\u7684\u8fb9\u957f\u7531acm\u589e\u52a06cm\uff0c\u5219\u6b63\u65b9\u5f62\u7684\u9762\u79ef\u589e\u52a0\u4e86\uff08 \uff09 A. 36cm2 B. 12acm2 C.\uff0836+12a\uff09cm2 D.\u4ee5\u4e0a\u90fd\u4e0d\u5bf9
每一项因数都可以看做平方差，例如1－1/2＾2利用平方差公式就等于(1-1/2)(1+1/2)因此此题就可以这么解答 注（平方差公式为a^2-b^2=(a+b)(a-b) )1-1/2^2)(1-1/3^2)....(1-1/10^2)
=(1-1/2)(1+1/2)(1-1/3)(1+1/3)....(1-1/10)(1+1/10)
=(1-1/2)(1-1/3)...(1-1/10)*(1+1/2)(1+1/3)...(1+1/10)
=(1/2)(2/3)...(9/10)*(3/2)(4/3)...(11/10)
=(1/10)(11/2)
=11/20
绛旓細(2+1)(2^2+1)(2^4+1)(2^8+1)+1 =1x(2+1)(2^2+1)(2^4+1)(2^8+1)+1 =(2-1)(2+1)(2^2+1)(2^4+1)(2^8+1)+1 =(2^2-1)(2^2+1)(2^4+1)(2^8+1)+1 =(2^4-1)(2^4+1)(2^8+1)+1 =(2^8-1)(2^8+1)+1 =2^16-1+1 =2^16 ...
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绛旓細(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15 =2*1/2*(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15 =2*(1-1/2)(1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15 =2*(1-1/2^2)(1+1/2^2)(1+1/2^4)(1+1/2^8)+1/2^15 =2...
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绛旓細骞虫柟宸叕寮锛屾槸鏁板鍏紡鐨勪竴绉嶏紝瀹冨睘浜庝箻娉曞叕寮忋佸洜寮忓垎瑙ｅ強鎭掔瓑寮忥紝琚櫘閬嶄娇鐢ㄣ傚钩鏂瑰樊鎸囦竴涓钩鏂规暟鎴栨鏂瑰舰锛屽噺鍘诲彟涓涓钩鏂规暟鎴栨鏂瑰舰寰楁潵鐨勪箻娉曞叕寮忥細a²-b²=(a+b)(a-b)銆傚仛棰樻楠わ細1銆佸厛鍒ゆ柇鑳藉惁浣跨敤骞虫柟宸叕寮忋傚垽鏂緷鎹細涓瀵圭浉绛夐」锛屼竴瀵圭浉鍙嶉」銆2銆佸鏋滃彲浠ヤ娇鐢紝鍒欎竴鑸儏鍐...
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庡畬鍏骞虫柟鍏紡缁煎悎杩愮敤鐨璁＄畻棰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
绛旓細銆璁＄畻杩囩▼銆戙愭湰棰樼煡璇嗙偣銆1銆骞虫柟宸叕寮銆備緥濡傦細6²-3²=(6-3)(6+3)=3脳9=27 (16-13)(16+13)=16²-13²=(3+13)²-13²=3²+2脳3脳13+13²-13²=9+78 =87 2銆佷箻娉曠粨鍚堝緥銆備箻娉曠粨鍚堝緥鏄箻娉曡繍绠楃殑涓绉嶏紝涔熸槸浼楀绠渚挎柟娉...
绛旓細(96+95)+鈥︹+(2-1)(2+1)=199+195+191+鈥︹+3 =(199+3)+(195+7)+(191+11)鈥︹=202+202+202+鈥︹=202脳(100梅4)=202脳25 =5050 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瓟棰樸傛湁涓嶆槑鐧界殑鍙互杩介棶锛佸鏋滄偍璁ゅ彲鎴戠殑鍥炵瓟銆傝鐐瑰嚮涓嬮潰鐨勩愰変负婊℃剰鍥炵瓟銆戞寜閽紝璋㈣阿锛
