冇番幾堂數學堂,呢幾條因式分解唔識做

5)

- (1/3) x²ⁿ⁺² - (1/27) x²ⁿ + (2/9) x²ⁿ⁺¹

= (- 1/27) x²ⁿ (9x² + 1 - 6x)

= (- 1/27) x²ⁿ (3x - 1)²


6)

6x - 6y - 9x² + 18xy - 9y² - 1

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

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

= (3x - 3y)² - 2(3x - 3y) + 1

= (3x - 3y - 1)²


7)

1 + a + b + c + ab + bc + ac + abc

= (a + ab + ac + abc) + (1 + b + c + bc)

= a (1 + b + c + bc) + (1 + b + c + bc)

= (a + 1) (1 + b + c + bc)

= (a + 1) ( 1 + c + b(1 + c) )

= (a + 1) (b + 1) (c + 1)


8)

a³ (a - 2b) - b³(b - 2a)

= (a - 2b) (a³ + b³)

= (a - 2b) (a + b) (a² - ab + b²)


2011-09-19 22:53:18 補充：
6) 打漏了負號 :

6x - 6y - 9x² + 18xy - 9y² - 1

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

= - [ ( (3x)² - 2(3x)(3y) + (3y)² ) - 2(3x - 3y) + 1 ]

= - [ (3x - 3y)² - 2(3x - 3y) + 1 ]

= - (3x - 3y - 1)²