F.2數學6條.20分.急████████████████████████

1.4a^2(y-2)^2-a^2
=4a^2(y^2+4)-a^2
=4a^2y^2+16a^2-a^2
=4a^2y^2+15a^2

2.48+24(2m-1)+3(2m-1)^2
=48+48m-24+3(4m^2-1)
=48+48m-24+12m^2-1
=23+48m+12m^2

3.y^2-x^2-2xy-2y^2
=-y^2-x^2-2xy

4. 25(3x-2y)^2-9(2x+y)^2
=25(9x^2+4y^2)-9(4x^2+y^2)
=225x^2+100y^2-36x^2-9y^2
=189x^2+91y^2

5.(a^2+b^2)^2-4a^2b^2唔知你想點?(-4a^2(+-*/)b^2)?

6.12(c^2+2)-2(c^2+2)^2-18
=12c^2+24-2(c^4+4)-18
=12c^2+24-2c^4-8-18
=12c^2-2c^4+24-8-18
=12c^2-2c^4-2

1. 4a^2(y-2)^2-a^2
=a^2[4(y-2)^2-1]
=a^2[2(y-2)+1][2(y-2)-1]
=a^2(2y-3)(2y-5)

2. 48+24(2m-1)+3(2m-1)^2
let (2m-1) be x,
=3x^2+24x+48
=3(x^2+8x+16)
=3(x+4)^2
=3(2m-1+4)^2
=3(2m+3)^2

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

4. 25(3x-2y)^2-9(2x+y)^2
=25(9x^2-12xy+4y^2)-9(4x^2+4xy+y^2)
=225x^2-300xy+100y^2-36x^2-36xy-9y^2
=189x^2-336xy+91y^2
=7(27x^2-48xy+13y^2)
=7(9x-13)(3x-1)

5. (a^2+b^2)^2-4a^2b^2
=(a^4+2a^2b^2+b^4)-4a^2b^2
=a^4-2a^2b^2+b^4
=(a^2-b^2)^2

6. 12(c^2+2)-2(c^2+2)^2-18
Let (c^2+2) be x,
=-2x^2+12x-18
=-2(x^2-6x+9)
=-2(x-3)^2
=-2(c^2+2-3)^2
=-2(c^2-1)^2
=-2[(c+1)(c-1)]^2


2008-11-27 21:49:56 補充：
5.
=(a^2-b^2)^2
=[(a+b)(a-b)]^2
=(a+b)^2(a-b)^2

6.
=-2[(c+1)(c-1)]^2
=-2(c+1)^2(c-1)^2

2008-11-27 21:51:28 補充：
eternalsonw's answers are not satisfactory.It hadn't been factorized in each of question.It hasn't finished.Please notice.

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