文档介绍：乘法公式: (x+a)(x+b)= x 2 +(a+b)x+ ab (a+b)(a-b)=a 2 -b 2——平方差公式 a=-b 时 ( ) A. (x-6)(x+6)=x 2 -6 B. (3x-1)(3x+1)=3x 2 -1 C. (-1+x)(-1-x)=x 2 -1 D. (5ab+1)(5ab-1)=25a 2b 2 -1 : 1) ( )( ) = m 2 -n 2 2) (2m-1)( ) = 4m 2 -1 3) (-2m+1)( ) = 1-4m :( a+2b+3)(a+2b-3) D 2m+1 m-n m+n 2m+1 :( a+2b+3)(a+2b-3) 解:原式= [ ( a+2b)+3][(a+2b)-3] = (a+2b) 2 -3 2 = (a+2b)(a+2b)-9 = a 2 +2ab+2ab+4b 2 -9 = a 2 +4ab+4b 2 -9 计算:( a+b) 2 , (a- b) 2解: ( a+b) 2 = (a+b) (a+b) =a 2+ab +ab +b 2 =a 2 +2ab+b 2 (a-b) 2 = (a-b) (a-b) =a 2-ab -ab +b 2 =a 2 -2ab+b 2完全平方公式(a+b) 2 =a 2 +2ab+b 2 (a-b) 2 =a 2 - 2ab+b 2 两数和(或差)的平方,等于它们的平方和,加上(或者减去)它们的积的2倍. 完全平方公式(a+b) 2 =a 2 +2ab+b 2 (a-b) 2 =a 2 - 2ab+b 2 bb aa abab a 2b 2baba (a-b) 2ab ab ( a+b) 2 =a 2 +2ab+b 2 , (a -b) 2 =a 2 -2ab+b 2 :( x+2y) 2 , (x-2y) 2解:( x+2y) 2= ( a+ b) 2 =a 2 +2 a b+ b 2 =x 2 +4xy+4y 2 (x - 2y ) 2= (a - b ) 2 =a 2 - 2 a b + b 2x 2 - 2 · x· 2y +( 2y ) 2 x 2 +2 ·x· 2y+(2y) 2 =x 2 - 4xy+4y 2解: 1) ( 4a-b) 2 = (4a) 2 -2·4a· b+b 2 = 16a 2 -8ab+b 2 3) (-2x-1) 2 =[-(2x+1)] 2 =(2x+1) 2 = (2x) 2 +2 ·2x· 1+1 =4x 2 +4x+1 :1)( 4a-b) 22) (y+ ) 23) (-2x-1) 2 2 1 2) (y+ ) 2 2 14 1 = y 2 +y+ 练****P130-1 =y 2 +2 ·y· +( ) 2 2 12 : 1) 102 2 2) 199 2 3) 498 2 4) 2解: 1) 102 2 = (100+2) 2 = 100 2 +2 ×100 × 2+2 2 = 10000+400+4 = 10404 2)199 2 = (200-1) 2 =200 2 -2×200 × 1+1 2 = 40000-400+1 = 39601