999緊急超易Factorize聽日交!!!

1. m² + n² + 3m - 3n
= m² + 3m + n² - 3n
= m (m +3) +n (n-3)

2. 18x² - 2y² -6x +2y
= 18x² -6x - 2y² +2y
= 6x(2x-1) -2y( y-1)

3. a³ - b³ - a² +b²
= (a³ - b³) - a² +b²
= (a-b) (a² +ab +b²) +b² - a²
= (a-b) (a² +ab +b²) +(b+a) (b-a)
= (a-b) (a² +ab +b²) -(b+a) (a-b)
= (a-b) [ (a² +ab +b²) -(b+a)]
= (a-b) (a² +ab +b² -b-a)

2008-04-07 00:19:21 補充：
Here are some identities.

(a+b)(a-b) = a² - b²
(a+b)² = a² +2ab +b²
(a-b)² = a² -2ab +b²
(a³ - b³)= (a-b) (a² +ab +b²)
(a³ +b³)= (a+b) (a² -ab +b²)

You can use the above identities to solvethe factorization.

18x²-2y²-6x+2y
=2(9x²-y²-3x+y)
=2[(9x²-y²)-(3x-y)]
=2[(3x+y)(3x-y)-(3x-y)]
=2(3x-y)(3x+y-1)

a³-b³-a²+b²
=(a³-b³)-(a²-b²)
=(a-b)(a²+ab+b²)-(a+b)(a-b)
=(a-b)(a²+ab+b²-a-b)

m^2 + n^2 + 3m -3n
=(m+n)^2 + 3(m-n)
=3(m-n)(m+n)^2
=3(m+n)(m+n)(m-n)
=3(m+n)(m-n)//

2008-04-07 00:03:43 補充：
18x² - 2y² -6x +2y
=2(3x-y)^2 -2(3x-y)
=(3x-y)(2-2)//

a³ - b³ - a² +b²
= (a-b)^3 -(a-b)^2
= ( a^2 +ab -b^2) - ( a^2 -2ab+b^2)//

[sorry that i'm not sure the ans is correct or not, but hope it can help]