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# 15.2.1平方差公式1

15.2.1

? (x+1)(x-1) =x2-x+x-1 =x2-1 ? (m+2)(m-2) =m2-2m+2m-22 =m2-22 =m2-4 ? (2x+1)(2x-1) =(2x) 2-2x+2x-1 =(2x) 2-1 =4x 2-1

2-b2 (a+b)(a-b)=a

a

b b

b

a

(1) (3x+2) (3x-2); (3) (-x+2y) (-x-2y).
(3x+2) (3x - 2) = (3x)2 - 22

(2) (b+2a)(2a-b);

(a + b) (a - b) = a2 - b2

(2) (b+2a)(2a-b) (3)(-x+2y)(-x-2y) =(2a+b)(2a-b) = (-x)2-(2y)2 =(2a)2-b2 2 2

=x -4y .

=4a2-b2

(1)(x+2)(x-2)= x2-2 x2-4 (2)(-3a-2)(3a-2)= 9a2-4 4-9a2

(1) 102×98;
(2) (y+2) (y-2) – (y-1) (y+5) .

= 1002-22=10 000 – 4 = 9 996. (2)(y+2)(y-2)- (y-1)(y+5) = y2-22-(y2+4y-5)
= y2-4-y2-4y+5

= - 4y + 1.

? ( a+b)(-b+a) ? (3a+2b)(3a-2b) ? (a5-b2)(a5+b2) ? (a+b)(a-b)(a2+b2)
a2-b2 9a2-4b2 a10-b4 a4-b4

? 算一算： 5x ? （x+y )( x-y)+(2x+y )( 2x-y） 2-2y2 -3x+49 ? x(x-3)-(x+7)(x-7) 填一填: ? （__+__）（__-__）= - 9 ? （a+2b+2c）（a+2b-2c）写成平方差 公式形式：_______________ (a+2b)2-(2c)2

1.下面各式的计算对不对?如果不对, 应当怎样改正? (1)(x+2)(x-2) = x2-2 ;
(2) (-3a-2) (3a-2) = 9a2 -4 .

2.运用平方差公式计算.
(1)(a+3b) (a-3b);

(2) (2) (3+2a) (-3 + 2a) ;
(3) 51×49; (4) (3x+4)(3x-4) – (2x+3) (3x-2).

?(a+b)(a-b)=a2-b2 两个数的和与这两个数的差的积等于 这两个数的平方差。
?平方差公式中字母 a、b可代表一个数、一个单 项式或多项式。

B. (a+b)2=a2+2ab+b2 C. (a-b)2=a2-2ab+b2 D. (a+2b)(a-b)=a2+ab-2b2
b

b

.计算 20042-2003×2005;