(F.2 )Factorize: 18a^2+15b-50b^2-9a

18a^2+15b-50b^2-9a
=18a^2-50b^2+15b-9a
=2(9a^2-25b^2)+3(5b-3a)
=2(3a+5b)(3a-5b)-3(3a-5b) [ By a^2 - b^2 = ( a + b )( a - b ) ]
=(3a-5b)[2(3a+5b)-3]
=(3a-5b)(6a+10b-3)

2007-11-14 21:42:07 補充：
Some additions: Step 1: 18a^2-50b^2+15b-9a ---> Grouping of terms Step 2 : 2(9a^2-25b^2)+3(5b-3a) --- > Take out common factors

18a^2+15b-50b^2-9a
= (18a^2 - 50b^2) - (9a - 15b)
= 2(9a^2 - 25b^2) - 3(3a - 5b)
= 2[(3a)^2 - (5b)^2] - 3(3a - 5b)
= 2(3a + 5b)(3a - 5b) - 3(3a - 5b)
= (3a - 5b)[2(3a + 5b) - 3]
= (3a - 5b)(6a + 10b - 3)