分解因式
4(a+b)^2-9(a-b)^2
分解因式 4(a+b)^2-9(a-b)^2
2006-10-15 2:51 pm
回答 (4)
2006-10-15 3:40 pm
✔ 最佳答案
上面的網友已經好努力，但可以進一步得到因子分解如下：4(a+b)^2-9(a-b)^2
= 4(a^2 + 2ab + b^2) - 9(a^2 - 2ab + b^2)
= 4a^2 + 8ab + 4b^2 - 9a^2 + 18ab - 9b^2
= -5a^2 + 26ab - 5b^2
= (5a - b) ( 5b - a)
2006-10-15 7:06 pm
(2^2)[(a+b)^2] - (3^2)[(a-b)^2]
=[2(a+b)]^2 - [3(a-b)]^2
=[2(a+b) + 3(a-b)] [2(a+b) - 3(a-b)]
=[2a+2b+3a-3b] [2a+2b-3a+3b]
=(5a-b)(5b-a)
=[2(a+b)]^2 - [3(a-b)]^2
=[2(a+b) + 3(a-b)] [2(a+b) - 3(a-b)]
=[2a+2b+3a-3b] [2a+2b-3a+3b]
=(5a-b)(5b-a)
2006-10-15 6:08 pm
4(a+b)^2-9(a-b)^2
=(2a+2b)^2-(3a-3b)^2
=(2a+2b+3a-3b)(2a+2b-3a+3b)
=(5a-b)(-a+5b)
=(5a-b)(5b-a)
=(2a+2b)^2-(3a-3b)^2
=(2a+2b+3a-3b)(2a+2b-3a+3b)
=(5a-b)(-a+5b)
=(5a-b)(5b-a)
2006-10-15 3:22 pm
4(a+b)^2-9(a-b)^2
= 4(a^2 + 2ab + b^2) - 9(a^2 -2ab+b^2)
= 4a^2 - 9a^2 + 2ab + 18ab + b^2 -9b^2
= -5a^2 + 20ab - 8b^2
2006-10-15 07:28:01 補充：
4(a b)^2-9(a-b)^2= 4(a^2 2ab b^2) - 9(a^2 -2ab b^2)= 4a^2 - 9a^2 8ab 18ab 4b^2 -9b^2= -5a^2 26ab - 5b^2
= 4(a^2 + 2ab + b^2) - 9(a^2 -2ab+b^2)
= 4a^2 - 9a^2 + 2ab + 18ab + b^2 -9b^2
= -5a^2 + 20ab - 8b^2
2006-10-15 07:28:01 補充：
4(a b)^2-9(a-b)^2= 4(a^2 2ab b^2) - 9(a^2 -2ab b^2)= 4a^2 - 9a^2 8ab 18ab 4b^2 -9b^2= -5a^2 26ab - 5b^2
收錄日期: 2021-04-13 13:42:24
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https://hk.answers.yahoo.com/question/index?qid=20061015000051KK00807