fully factorise: 56a^3+189b^3?

2009-03-18 9:48 am
I worked out an answer but I'm not totally sure if it's right, please do step by step working out.

If you you need the formula it is: (a+b)(a^2-ab+b^2)
更新1:

sincere apologies, can you also work out 16^4-y^4 I'm oficially stuck on two questions GAH

回答 (2)

2009-03-18 10:01 am
✔ 最佳答案
1)
56a^3 + 189b^3
= 7(8a^3 + 27b^3)
= 7[(2a)^3 + (3b)^3]
= 7[2a + 3b][(2a)^2 - (2a)(3b) + (3b)^2]
= 7[2a + 3b][4a^2 - 6ab + 9b^2]

2)
a^2 - b^2 = (a + b)(a - b)

16x^4 - y^4
= (2x)^4 - y^4
= (4x^2)^2 - (y^2)^2
= [4x^2 + y^2][4x^2 - y^2]
= [4x^2 + y^2][(2x)^2 - y^2]
= [4x^2 + y^2][2x + y][2x - y]
2009-03-18 5:04 pm
56a^3+189b^3
=7(8a^3+27b)
=7(2a+3b)(4a^2-6ab+9b^2) answer//

16^4-y^4=(4^2+y^2)(4^2-y^2)
=(16+y^2)(16-y^2)
=(16+y^2)(4+y)(4-y) answer//


收錄日期: 2021-05-01 12:09:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20090318014806AAtnUAq

檢視 Wayback Machine 備份