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# 平方差公式课件

§2.1

m2 - 4 (2) (m+2)(m-2) =
(3) (2x+1)(2x-1) = 4x2 - 1

(a+b)(a-b) =

2-b2 a

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

§2.1

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

a

a

b

a-b
a

(a+b)(a-b)

b

b

a-b

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

a

a

2 a

a

a

2-b2 a
b
b

a
1 (a+b)(a-b) 2

a
1 (a+b)(a-b) 2

b
b

a

(a+b)(a-b)
a

=
2-b2 a

b
b

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

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

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

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

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

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

(相同项)2-(相反项)2

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

1.下列各式中,能用平方差公式运算的是( A ) A.(-a+b)(-a-b) B.(a-b)(b-a)

C.(2a-3b)(3a+2b)

D.(a-b+c)(b-a-c)

2.下列多项式相乘,不能用平方差公式计算的是(C) A.(x-2y)(2y+x) C.(-2y-x)(x+2y) B.(-x+2y)(-x-2y) D.(-2b-5)(2b-5)

⑴ (3x+2)(3x-2) ; ⑵ (b+2a)(2a-b); (3) (-x+2y)(-x-2y).

⑴ (3x+2)(3x-2) = (3x)2 - 22 3x 2 3x 2

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

3x 2 3x 2 ⑴ (3x+2)(3x-2) (3x)2 - 22 = = 9x2 - 4 b+2a 2a-b ⑵ (b+2a)(2a-b); 2a b 2a b =(2a+b)(2a-b) =(2a)2- b2 =4a2 – b2 (3) (-x+2y)(-x-2y) = (-x)2-(2y)2 = x2-4y2

(1) (x+2)(x-2) = x2 - 2 (2) (-3a-2)(3a-2) = 9a2 X2 - 4 4 4 - 9a2

ㄨ ㄨ

(2) (3+2a)(-3+2a) = 4a2 - 9

98 ⑴ 102 ×98 = (100+2) (100-2) = 1002-22 = 10000-4 = 9996

y 2 y2 y1 y 5 ⑵ (y+2)(y-2)-(y-1)(y+5)

= y2 - 22 - (y2+4y-5)
= y2-4-y2-4y+5 = -4y+1

1、(m+n)(-n+m) =
2、(-x-y) (x-y) =

m2-n2 y2-x2 4a2-b2 x4-y4

3、(2a+b)(2a-b) = 4、(x2+y2)(x2-y2)=

5、 51 × 49

=

2499

1、(3x+4)(3x-4) – (2x+3)(3x-2); 2、(x+y)(x-y)(x2+y2);

(2+1)(22+1)(24+1)(28+1) … (22n+1)

= (22-1)(22+1)(24+1) = (24-1)(24+1) = 28-1

(2+1)(22+1)(24+1)(28+1) … (22n+1) 的结果吗？