因式分解~20分~急

1. x^2-25
解：x^2-25
=x^2-5^2
=(x+5)(x-5)

2. 4x^2-1
解：4x^2-1
=(2x)^2-1^2
=(2x+1)(2x-1)

3. 9x^2-25
解：9x^2-25
=(3x)^2-5^2
=(3x+5)(3x-5)

4. 49x^2-100
解：49x^2-100
=(7x)^2-10^2
=(7x+10)(7x-10)

5. 4x^2-9y^2
解：4x^2-9y^2
=(2x)^2-(3y)^2
=(2x+3y)(2x-3y)

6. 2x^2-50
解：2x^2-50
=2(x^2-25)
=2(x+5)(x-5)

7a.x^2+4x+4
解：x^2+4x+4
=x^2 + 2*2*x^2 + 2^2
=(x+2)^2

b.x^2+4x+4y-y^2
解：x^2+4x+4y-y^2
=(x^2-y^2)+(4x+4y)
=(x+y)(x-y)+4(x+y)
=(x+y)(x-y+4)

8a. x^2+4xy+4y^2
解：x^2+4xy+4y^2
=(x+2y)^2

b. x^2+4xy+4y^2-z^2
解：x^2+4xy+4y^2-z^2
=(x^2+4xy+4y^2)-z^2
=(x+2y)^2-z^2
=(x+2y+z)(x+2y-z)

2010-08-30 13:25:09 補充：
9a. r^2-10rs+25s^2
解：r^2-10rs+25s^2
=r^2-2*r*5s+(5s)^2
=(r-5s)^2

b. r^2-10rs+25s^2-t^2
解：r^2-10rs+25s^2-t^2
=(r-5s)^2-t^2
=(r-5s+t)(r-5s-t)

1. ( x + 5 ) ( x - 5 )
2. ( 2x + 1 ) ( 2x - 1 )
3. ( 3x + 5 ) ( 3x - 5 )
4. ( 7x + 10 ) ( 7x - 10 )
5. ( 2x - 3y ) ( 2x + 3y )
6. 2 ( x + 5 ) ( x - 5 )

2010-08-30 13:19:27 補充：
7a.x^2+4x+4

= ( x + 2 ) ^ 2

2010-08-30 13:22:05 補充：
8a. x^2+4xy+4y^2

= ( x + 2y ) ^2

2010-08-30 13:22:29 補充：
9a. r^2-10rs+25s^2

= ( r + 5s ) ^ 2