因式分解---利用恆等式

As follows:


圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/28-3.jpg



圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/29-2.jpg

1. 125y^2 - 20x^2
=5(25y^2 - 4x^2)
=5(5y-2x)(5y+2x)

2. (a+b)^2 - 9a^2b^2
=(a+b)^2 - (3ab)^2
=(a+b-3ab)(a+b+3ab)

3. 3x^2 - 243
=3(x^2-81)
=3(x-9)(x+9)

4. x^2 + 10x + 25 - 4y^4
=(x^2 + 10x + 25) - 4y^4
=(x+5)^2 - (2y)^2
=(x+5-2y)(x+5+2y)

5. x^2 - 2xy - 3y^2
=(x^2 - 2xy + y^2) - 4y^2
=(x-y)^2 - (2y)^2
=(x-y-2y)(x-y+2y)
=(x-3y)(x+y)

6. x^2 - y^2 + 2x -4y - 3
=(x^2 - y^2) + (2x - 4y) - 3
=(x-y)(x+y) + 2(x-2y) - 3

2010-09-26 17:23:21 補充：
Sorry for no. 6

x^2 - y^2 + 2x -4y - 3
= (x^2 + 2x + 1) - (y^2 + 4y + 4)
= (x+1)^2 - (y+2)^2
= (x+1-y-2)(x+1+y+2)
= (x-y-1)(x+y+3)

(5) x^2 -2xy-3y^2
=x^2 -2xy +y^2 -4y^2
=(x-y)^2-(2y)^2
=(x-y+2y)(x-y-2y)
=(x+y)(x-3y)