1522完全平方公式

1、完全平方公式,計(jì)算下列各式, 你能發(fā)現(xiàn)什么規(guī)律? (p+1)2 = (p+1) (p+1) = _ (m+2)2= _; (p-1)2 = (p-1 ) (p-1) = _; (m-2)2 = _.,p2+2p+1,m2+4m+4,p2-2p+1,m2-4m+4,探究,我們來(lái)計(jì)算(a+b)2, (a-b)2.,(a+b)2=(a+b) (a+b) = a2+ab+ab+b2 =a2+2ab+b2. (a-b)2 = (a-b) (a-b) = a2-ab-ab+b2 =a2-2ab+b2,一般地, 我們有 即兩數(shù)和(或差)的平方,等于它們的平方和,加(或減)它們的積的2倍. 這兩個(gè)公式叫做(乘

2、法的)完全平方公式.,(a+b)2=a2+2ab+b2, (a-b) 2 = a2-2ab +b2.,你能根據(jù)圖15.3 -2和圖15.3 -3 中的面積說(shuō)明完全平方公式嗎?,思考,例3 運(yùn)用完全平方公式計(jì)算: (1) (4m+n)2; (2) (y- )2.,解: (1) (4m+n) 2= (4m)2 + 2(4m)n+n2 = 16m2+8mn +n2; (2) (y - )2 = y2 - 2y + ( )2 = y2-y +,例題,例4 運(yùn)用完全平方公式計(jì)算: (1) 1022 ; (2) 992 .,解: (1) 1022 = (100 +2) 2 = 1002 +2 100 2

3、+ 22 = 10 000 +400 +4 = 10 404 .,(2) 992 = (100 -1)2 = 1002 -2100 1+12 = 10 000 - 200 + 1 = 9 801.,例題,(a+b)2與(-a-b)2相等嗎? (a-b)2與(b-a)2相等嗎? (a-b)2與a2-b2相等嗎? 為什么?,思考,1.運(yùn)用完全平方公式計(jì)算: (1)(x+6)2; (2) (y-5)2 ; (3) (-2x+5)2; (4) ( x - y)2. 2.下面各式的計(jì)算錯(cuò)在哪里?應(yīng)當(dāng)怎樣改正? (1) (a+ b)2 = a2 +b2; (2) (a b) 2 =a2 b2.,練習(xí),添括

4、號(hào)時(shí),如果括號(hào)前面是正號(hào),括到括號(hào)里的各項(xiàng)都不變號(hào);如果括號(hào)前面是負(fù)號(hào),括到括號(hào)里的各項(xiàng)都改變符號(hào).,a+(b+c) = a+b+c; a- (b+c) = a - b c.,a + b + c = a + ( b + c) ; a b c = a ( b + c ) .,例5 運(yùn)用乘法公式計(jì)算: (1) ( x +2y-3) (x- 2y +3) ; (2) (a + b +c ) 2.,解: (1) ( x +2y-3) (x- 2y +3) = x+ (2y 3 ) x- (2y-3) = x2- (2y- 3)2 = x2- ( 4y2-12y+9) = x2-4y2+12y-9.,(a + b +c ) 2 = (a+b) +c 2 = (a+b)2 +2 (a+b)c +c2 = a2+2ab +b2 +2ac +2bc +c2 = a2+b2+c2 +2ab+2bc +2ac.,例題,1.在等號(hào)右邊的括號(hào)內(nèi)填上適當(dāng)?shù)捻?xiàng): (1) a + b + c = a + ( ); a b c = a ( ) ; a - b + c = a ( ); a + b + c = a - ( ).,能否用去括號(hào)法則檢查添括號(hào)是否正確?,練習(xí),2.運(yùn)用乘法公式計(jì)算: (a + 2b 1 ) 2 ;