數學問題(要詳細步驟)

1. x^4-6x^2+9
=y^2-6y+9 where(y=x^2)
=(y-3)^2
=(x^2-3)^2

2. x^4-6x^2+9-4x^2
from1.),=(x^2-3)^2-(2x)^2
=(x^2-3-2x)(x^2-3+2x)

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

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

4b. (x+1)^4+(x+1)^2+1
from a,=((x+1)^2-(x+1)+1)((x+1)^2+x+1+1)
=(x^2+2x+1-x)(x^2+2x+1+x+2)
=(x^2+x+1)(x^2+3x+3)

5.x^4-1=(x^2)^2-1
=(x^2+1)(x^2-1)
"=(x^2+1)(x+1)(x-1)"

6.x^3-27y^3not=(x-3y)^3
=x^3-(3y)^3
=(x-3y)(x^2+3xy+(3y)^2)

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


8. 8m²-24mn+18n²
=2(4m²-12mn+9n²)
=2(2m-3n)²

9. 1-2a²+a^4
=a^4-2a^2+1
=(a^2-1)^2
=((a+1)(a-1))^2

2007-07-22 22:23:41 補充：
d ans.是我做的,其他都是抄我

1. x^4-6x^2+9
=(x^2)^2 -6x^2 +9
(x^2-3)(x^2-3)
=(x^2-3)^2

2. x^4-6x^2+9-4x^2
=(x^2-3)^2-(2x)^2
=(x^2-3-2x)(x^2-3+2x)
=(x^2-2x -3 )(x^2+2x-3)
=(x+1)(x-3)(x-1)(x+3)


3. x^6-1
=(x^2)^3 -1
=(x^2-1)(x^4 +x^2+1)

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

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

5.Correct!
x^4-1=(x^2)^2-1
=(x^2+1)(x^2-1)
=(x^2+1)(x+1)(x-1)

6.you are wrong~
x^3-27y^3
=x^3-(3y)^3
=(x-3y)(x^2+3xy+(3y)^2)

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


8. 8m²-24mn+18n²
=(2m-3n)(4m-6n)

9. 1-2a²+a^4
=a^4-2a^2+1
=(a^2-1)^2
=((a+1)(a-1))^2

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