中五數學~請幫助~

2009-09-21 5:29 am
把下列各式因式分解

1.) 12a^3 b^2 c^4 - 18a^2b^4

2.) 15x^-10x^2

3.) - 6a^3 + 15a^2 - 12a

4.) a^2+ ab+b+a

5.) x^3+4x^2+4x+16

6.) 10my - nx- 5ny + 2mx

7.) ab - bc - ac + b^2

8.) abc^2 + abd^2 + cda^2 + cdb^2

回答 (1)

2009-09-21 7:26 am
✔ 最佳答案
1.) 12a^3b^2c^4 - 18a^2b^4
= 6a^2b^2(2ac^4 - 3b^2)
2.) 15x^ -10x^2
Question incomplete. Do not know the power after 15x^
3.) - 6a^3 + 15a^2 - 12a
= -3a(2a^2 - 5a + 4)
4.) a^2 + ab + b + a
= a(a + b) + (a + b)
= (a + 1)(a + b)
5.) x^3 + 4x^2 + 4x + 16
= x^2(x + 4) + 4(x + 4)
= (x^2 + 4)(x + 4)
6.) 10my - nx - 5ny + 2mx
= 10my + 2mx - 5ny - nx
= 2m(5y + x) - n(5y + x)
= (2m - n)(5y + x)
7.) ab - bc - ac + b^2
= ab + b^2 - ac - bc
= b(a + b) - c(a + b)
= (a + b)(b - c)
8.) abc^2 + abd^2 + cda^2 + cdb^2
= abc^2 + cda^2 + abd^2 + cdb^2
= ac(bc + ad) + bd(ad + bc)
= (ac + bd)(ad + bc)


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