factorize , thank!

2006-12-01 3:13 am
Factorize

1) a^3-a^2-a+1

2) (a^2-1)^2-(1-2a)^2

3) 25(x^2-y^2)-10x+1

唔該要步驟

回答 (1)

2006-12-01 10:34 pm
✔ 最佳答案
1
a^3-a^2-a+1
=a^2(a-1)-a+1
=a^2(a-1)-(a-1)
=(a-1)(a^2-1)
=(a-1)(a-1)(a+1)
=(a-1)^2(a+1)
2
(a^2-1)^2-(1-2a)^2
=(a^2-1+1-2a)(a^2-1-1+2a)
=(a^2-2a)(a^2+2a-2)
=a(a-2)(a^2+2a-2)
3
25(x^2-y^2)-10x+1
=25x^2-25y^2-10x+1
=25x^2-10x+1-25y^2
=(5x-1)^2-25y^2
=(5x-1+5y)(5x-1-5y)




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