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# 3.4乘法公式(1) 浙教版2014

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1

2
1

(a+n)(b+m)= ab +am+nb +mn
3 4
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2

3

4

a ?4 (1) (a+2)(a-2)=_____________
2

(2) (3-x)(3+x)=_____________ 9? x
2
2 2 a ? b (3) (a+b)(a-b )=_____________

2 2 (4) (2m+n)(2m-n)=__________ 4m ? n

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b
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a a a b

a-b

b

b
2 2

a ? b)(a ? b) 新长方形的面积为：( _________________

a ?b 原图形实际面积为：________________
(a ? b)(a ? b) ? a ? b
2
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2

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

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25-36x2 (1)(5+6x)(5-6x)=( 5 )2-( 6x)2=______ (2)(x-2y)(x+2y)=( x )2-( 2y)2=_______ x2-4y2 (3)(-m+n)(-m-n)=(-m )2-( n )2=_______ m2-n2

? 注意 准确确定a和b ①利用平方差公式计算的关键是__________

②当分数或是数与字母的乘积时,要用括号把这个数

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

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2 – ___2 =____ (1)(3x+5y)(3x-5y) =___ 9x2-25y2 (5y) (3x)

1 1 (2) ( b ? a)( ? b ? a) 2 2 1 1 ? (a ? b)( a ? b) 2 2
1 2 ? a ? ( b) 2 1 2 2 ?a ? b 4
2

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（1）（x+1)(x-1) = x2-1

(2)
(3)

(x+2)(x-2)

=

X2

- 4

(-m+n)(-m-n) =(-m)2-n2 =m2-n2

(4)
(5)

(m+6)(m-6) =m2 - 6 2 = m2-36
(x+2y)(x-2y) =x2-(2y)2=x2-4y2

(6)
(7)

(3x-2)(3x+2) =(3x)2-22=9x2-4
(b+5a)(b-5a) = b2 - (5 a )2 =b2 - 25a 2
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2、用平方差公式计算下列各式 (1) ( y ? x)( x ? y )
2 2

(2)( 2a ?
2

3b)( 2a ?
2

3b)

? ( 2a ) ? ( 3b) ? 2a ? 3b
2 2

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(1)103×97 =(100+3)(100-3)
=1002-32 =10000-9

=9991

(2)59.8×60.2 =(60-0.2)(60+0.2) =602-0.22 =3600-0.04

=3599.96
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2 1 (3)50 ? 49 3 3

6 1 (4)10 ?11 7 7

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