如題，
因數分解問題:a^6k^6-1
數學書中寫了答案是: (ak+1)(ak-1)(a^2k^2-ak+1)(a^2k^2+ak+1)
但我不知為何會得出這個答案，請列出步驟，謝謝！
一條因數分解問題不懂！
2009-01-13 4:30 am
回答 (2)
2009-01-13 5:06 am
✔ 最佳答案
a^6k^6-1=(ak)^6-1
=((ak)^3-1^3)((ak)^3+1^3)
=(ak-1)(a^2k^2+ak+1)(ak+1)(a^2k^2-ak+1)
=(ak+1)(ak-1)(a^2k^2-ak+1)(a^2k^2+ak+1)
note:
a^3-b^3=(a-b)(a^2+ab+b^2)
a^3+b^3=(a+b)(a^2-ab+b^2)
2009-01-13 5:05 am
設x= ak
a^6k^6-1=x^6-1
=(x^3)^2- 1^2
=(x^3+1)(x^3-1)
=(x+1)(x^2-x+1)(x-1)(x^2+x+1)
=(ak+1)(a^2k^2- ak+1)(ak-1)(a^2k^2+ak+1)
a^6k^6-1=x^6-1
=(x^3)^2- 1^2
=(x^3+1)(x^3-1)
=(x+1)(x^2-x+1)(x-1)(x^2+x+1)
=(ak+1)(a^2k^2- ak+1)(ak-1)(a^2k^2+ak+1)
收錄日期: 2021-04-26 13:06:26
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090112000051KK01663