Maths problems! Help help!

1a) 8-6x-9x^2

- 9x^2 - 6x + 8


- 3x.............. 2
....... X
..3x.............. 4
---------------------------
- 3x*4 + 3x*2 = - 6x

Ans : (- 3x + 2)(3x + 4) = - (3x - 2)(3x + 4)


1b)
-6x^2+6xy=12y^2

If the question is -6x^2 + 6xy - 12y^2


-3x............ 6y
......... X
.2x........... -2y
------------------------------

-3x(-2y) + 2x*6y = 6xy


Ans : (-3x + 6y)(2x - 2y) = 0

3(2y - x) 2(x - y) = 0

6(x - y)(2y - x) = 0

or

6(x - y)(x - 2y) = 0


1c) 4x^2-(y^2-2y+1)

= 4x^2 + 0 - (y^2 - 2y + 1)


2x................. - (y - 1)
........... X
2x.................. (y - 1)
____________________
2x(y - 1) - (y - 1)2x = 0


Ans : [2x - (y - 1)] (2x + y - 1)

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


1d) 16(x+y)^2+24(x+y)z=9z^2

If the questions is 16(x+y)^2 + 24(x+y)z + 9z^2 = 0



4(x+y)................... 3z
..................X
4(x+y)................... 3z
------------------------------------------
4(x+y)*3z + 4(x+y)*3z = 24(x+y)z


Ans : [4(x+y) + 3z][4(x+y) + 3z]

= [4(x+y) + 3z]^2

= (4x + 4y + 3z)^2





2010-07-13 17:23:56 補充：
1b)

Ans : (-3x + 6y)(2x - 2y)

3(2y - x) 2(x - y)

6(x - y)(2y - x)

2010-07-13 17:32:42 補充：
If the question of 1b) is -6x^2 + 6xy + 12y^2 ,

-6x 12y
X
x y
____________

-6x * y + 12yx = 6xy ,

Ans : (-6x + 12y)(x + y)

= - 6(x - 2y)(x + y)

or = 6(2y - x)(x +y)

2010-07-13 17:35:02 補充：
走了位 , 打多次條式 :

-6x......12y
.......X
x .........y
____________

-6x * y + 12yx = 6xy

8-6x-9x^2
-(9x+6x-8)
-(3x-2)(3x+4)
(2-3x)(3x+4)
_____________________
-6x^2+6xy-12y^2
-6(x^2-xy+2y^2)
________________________
4x^2-(y^2-2y+1)
4x^2-(y-1)^2
(2x-y+1)(2x+y-1)
________________________
16(x+y)^2+24(x+y)z-9z^2
(4x+4y+9z)(4x+4y-3z)