國中因式分解？
回答 (2)
2013-01-12 3:36 am
✔ 最佳答案
Set m=a+b，n=ab(a+b)(a+1)(b+1)+ab
=(a+b)(ab+a+b+1)+ab
=m*(n+m+1)+n
=mn+m^2+m+n
=(mn+n)+(m^2+m)
=n(m+1)+m(m+1)
=(m+n)(m+1)
=(a+b+ab)(a+b+1)
2013-01-12 2:52 am
(a+b)(a+1)(b+1)+ab
= (a + b)(ab + a + b + 1) + ab
= a^2b + a^2 + ab + a + ab^2 + ab + b^2 + b + ab
= a^2 + b^2 + 2ab + a^2b + ab^2 + a + b
= (a + b)^2 + ab(a + b) + a + b
= (a + b)(a + b + ab + 1)
=(a + b)[a(b + 1) + (b + 1)]
= (a + b)(a + 1)(b + 1)
= (a + b)(ab + a + b + 1) + ab
= a^2b + a^2 + ab + a + ab^2 + ab + b^2 + b + ab
= a^2 + b^2 + 2ab + a^2b + ab^2 + a + b
= (a + b)^2 + ab(a + b) + a + b
= (a + b)(a + b + ab + 1)
=(a + b)[a(b + 1) + (b + 1)]
= (a + b)(a + 1)(b + 1)
收錄日期: 2021-04-30 17:22:12
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https://hk.answers.yahoo.com/question/index?qid=20130111000015KK04060