math f.2~急!!!THX~~

1. x^2+5x+6
(x+3) (x+2)

2. x^2+4x+3
(x+3)(x+1)

3. x^2-3x-10
(x-5) (x+2)

4. 2x^2+3x-2
(2x-1) (x+2)

5. 2a^2+ab-3b^2
(2a+3b)(a-b)

6. -12-5x+2x^2
=2x^2 -5x -12
=(2x+3)(x-4)

7. 4x^2-14xy+6y^2
=2 (2x^2 -7xy +3y^2)
=2(2x-y)(x-3y)

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

9. 8b^3-1
= (2b)^3 - 1^3
= (2b-1)( (2b)^2 + (2b)(1) + (1)^2 ) by question 8
= (2b-1)(4b^2 + 2b +1)

10. 64x^3-y^3
=(4x)^3 - y^3
=(4x-y)(16x^2 + 4xy + y^2)

11. 5+135k^2
= 5(1+27k^2)

actually I think it is k^3 but not k^2
otherwise, the one is factorized.
If it is k^3, we can continue.
5+135k^3
=5(1+27k^3)
=5( 1 + (3k)^3 )
as we know x^3 + y^3 = (x+y)(x^2-xy+y^2)
5( 1 + (3k)^3 )
= 5(1+3k)(1-3k+9k^2)

12. 27y^3+x^3y^3

13. (x+1)^3-x^3

2012-08-25 17:06:34 補充：
12. 27y^3+x^3y^3
=(3y)^3 + (xy)^3
=(3y+xy)(9y^2 -3xy^2 + x^2 y^2)

13. (x+1)^3-x^3
=(x+1-x) ( (x+1)^2 +(x+1)x + x^2 )
= (1) ( x^2 + 2x +1 + x^2 + x + x^2 )
= 3x^2 + 3x + 1

1. x^2+5x+6
=(x+2)(x+3)

2. x^2+4x+3
=(x+1)(x+3)

3. x^2-3x-10
(x-5)(x+2)

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

5. 2a^2+ab-3b^2
(a-b)(2a+3b)

6. -12-5x+2x^2
=2x^2-5x-12
=(x-4)(2x+3)

7. 4x^2-14xy+6y^2
=2(2x^2-7xy+3y^2)
=2(x-3y)(2x-y)

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

9. 8b^3-1
=(2b-1)(4b^2+2b+1)

10. 64x^3-y^3
=(4x-y)(16x^2+4xy+y^2)

11. 5+135k^2
=5(27k^2+1)
I think it should be 135k^3, then the steps should be as follows:
5+135k^3
=5(27k^3+1)
5(3k+1)(9k^2-3k+1)

12. 27y^3+x^3y^3
=y^3(x^3+27)
=y^3(x+3)(x^2-3x+9)

13. (x+1)^3-x^3
(x+1-x)(x^2+2x+1+x^2+x+x^2)
=3x^2+3x+1
3x^2+3x+1 cannot be further factorized.