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am

（a+b)(m+n) =

+an

+bm

+bn

• (x+1) (x-1) =

• (m+2)(m-2) =

• ③(2x+1)(2x-1) =

x2 - 1

m2 - 4

4x2 - 1

(a+b)(a-b)=

x2 - 1

• ① (x+1) (x-1) =

• (m+2)(m-2) =

• ③ (2x+1)(2x-1) =

m2 - 4

4x2 - 1

a2-b2

a2-ab+ab-b2

= a2-b2

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

a

a-b

a

a

b

b

b

b

a-b

b

(a+b)(a-b)

a2-b2

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

a

(a+b)(a-b)

(a+b)(a-b)

1

1

2

2

a2-b2

a

a

b

b

b

b

a2-b2

(a+b)(a-b)

=

15.3.1平方差公式

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

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

15.3.1 平方差公式

（ ）

① (-a+b)(a+b)

② (-a+b)(a-b)

③ (a+b)(a-c)

④ (2+a)(a-2)

⑤ (-0.25x-2y)(-0.25x+2y)

⑥ (1-x)(-x-1)

⑦ (a+b+c)(a+b-c)

（ ）

（ ）

（ ）

（ ）

（ ）

（ ）

⑴ (3x+2)(3x-2) ;

⑵ (b+2a)(2a-b);

(3) (-x+2y)(-x-2y).

(

)

(

)

+

⑴ (3x+2)(3x-2)

3x

2

(3x)2

2

3x

-

=

22

a

a

b

= a2 - b2

b

3x

⑴ (3x+2)(3x-2)

2

3x

2

-

(3x)2

22

=

= 9x2 - 4

+2a

⑵ (b+2a)(2a-b);

2a

b

-b

2a

2a

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

b

b

=(2a)2

b2

-

=4a2 – b2

(3) (-x+2y)(-x-2y)

= (-x)2-(2y)2

= x2-4y2

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

15.3.1 平方差公式

⑴ 102 ×98

⑵ (y+2)(y-2)-(y-1)(y+5)

= (100+2)(100-2)

= 1002-22

=9996

(2) (y+2)(y-2)-(y-1)(y+5)

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

= y2-4-y2-5y+y+5

= -4y+1

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

15.3.1平方差公式

1、(x+y)(x-y)(x2+y2);

2、(2+1)(22+1)(24+1)(28+1) … (22n+1)

• 谈一谈：你这一节课有什么收获？

①公式中的字母a、b可以表示数，也可表示式（单项式、多项式等）；

②要符合公式结构特征才能运用公式，否则仍用多项式相乘法则。