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# 乘法公式复习 - PowerPoint PPT Presentation

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

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

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

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

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

(相同项)2-(相反项)2

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

1、(-a+b)(a+b)

2、(x-y)(-x-y)

3、(a+5)(-5+a)

4、（萝卜+白菜）（萝卜-白菜）

2

2

=b -a

2

2

=y -x

2

=a -25

2

2

=萝卜 –白菜

1、请你判断以下的计算是否正确，并说明理由；

⑴、(m＋3n)(m－3n)=m²－3n² ( )

⑵、(－ m＋3n)(m－3n)=m²－9n² ( )

⑶、(－ m － 3n)(－ m ＋ 3n)=m²－9n² ( )

⑷、 (m－3n) ² = m²－9n² ( )

×

×

×

1、(a+4)( a-4) 2、(2x+2)(2x-2)

3、(-3a+1)(-3a-1) 4、(x +2y)(2y-x )

5. (a+b+1)(a+b-1) 6、(x+2)(x-2)(x +4)

2

2

=a -4

=a -16

2

2

=(2x) -2

=4x -4

2

2

3

3

2

2

2

2

=(-3a) -1

=9a -1

=(2y) -(x )

=4y -x

3

2

2

6

2

=[(a+b)+1][(a+b)-1]

=(a+b) -1

=a +2ab +b -1

=(x -4)(x +4)

=x -16

2

2

2

2

4

2

2

= (－2x)²－ (y)²

= 4x²－ y²

⑵ (－2x＋y)(2x＋y )

= (y)²－ (－2x)²

= y²－ 4x²

98×102

=(100-2)(100+2)

=100 -2

=10000-4

=9996

2

2

1. 100.5 x 99.5 2. 51 x 49

=100 - 0.5

=9999.75

=50 -1

=2499

2

2

2

2

2

1. 完全平方公式：

(a+b)2 = a2 + 2ab + b2

(a-b)2 = a2 - 2ab + b2

2. 口诀：

(1)(2x−3y)2＝2x2 - 2(2x)(3y)+3y2;

(2) (2x+3y)2＝4x2+ 9y2；

(3) (2x−3y)2＝(2x)2- 2(2x)(3y)+(3y)2.

(2)少了第一数与第二数乘积的2倍 (丢了一项) :2•(2x)•(3y);

(3) 用公式正确，只是计算要到最后结果

+2pq+q2

D

(A) (p+q)2=p2+q2

4

(B) (a+2b)2=a2+4ab+2b2

a2

(C) (a2+1)2=a4+2a+1

(D) (-s+t)2=s2-2st+t2

=

=

(- 2m - 3n )

( 2m + 3n )

[-( 2m + 3n )]

2

2

2

(1)( -2m - 3n )2 ;

(2m)

2

2

+ (3n)

= 4m + 12mn + 9n

2

2

+2(2m)·3n

=

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

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

1.(-x-y)2=

（x＋ y）2

＝x2＋2xy＋y2

2.(-2a2+b)2=

（2a2－b）2

＝4a4－4a2b＋b2

(1) (x+3)2 - x2

平方差公式单项式乘多项式.

完全平方公式 合并同类项

(x+3)2-x2

=x2＋6x+9-x2

=6x+9

(x+3)2-x2

=(x+3+x)(x+3-x)

=(2x+3)·3=6x+9

1、计算： (2a-b)2-(b+2a)2

=4a(-2b)

=-8ab

2、计算：(2a-b)2(b+2a)2

1、 计算： (2a-b)2+(b+2a)2

=8a2+2b2

① — ② 得：

（作差法）

（凑平方法）

2ab

（ ）

1、如果x2-6x+N是一个完全平方式,那么N是( )

(A )-3 (B)3 (C)-9 (D)9

D

C

2、如果x2-Nx+9是一个完全平方式,那么N是( )

(A )-6 (B)6 (C) ±6 (D) ±9

1、平方差公式： (a+b)(a-b)=a2-b2

2、完全平方公式：(a+b)2 = a2 + 2ab + b2

(a-b)2 = a2 - 2ab + b2

1、已知： ,

2、已知：

(a+b+c )

2

1、 计算 (a+b+c)2

2、计算： (a+b+2c) (a+b-2c)

3、已知 (a+b)2=25 ab=3 则 a2+b2=___

(2+1)(2 +1)(2+1)(2 +1) +1

2

4

8

=(2 -1)(2 +1)(2 +1)(2 +1)+1

=(2 -1)(2 +1)(2 +1)+1

=(2 -1)(2 +1)+1

=2 -1+1

=2

2

4

8

2

2

4

8

4

8

4

8

8

16

16

1、 (3 +1)(3 +1)(3 +1)(3 +1)(3 +1)

2、5(6+1)(6 +1)(6 +1)(6 +1)

4

8

16

2

=(3 -1)(3 +1)(3 +1)(3 +1)(3 +1) ÷2

=(3 -1)(3 +1)(3 +1)(3 +1) ÷2

=(3 -1)(3 +1)(3 +1) ÷2

=(3 -1)(3 +1) ÷2

=

2

4

8

16

2

2

4

8

16

4

4

8

16

8

8

16

16

16

32

3

2

2

4

8

2

4

8

=(6 -1)(6 +1)(6 +1)(6 +1)

=(6 -1)(6 +1)(6 +1)

=(6 -1)(6 +1)

=6 -1

2

2

4

8

4

4

8

8

8

16