因式分解問題..唔識做 (x^2+8x+17)^2-(2x+8)^2?
回答 (2)
2017-11-09 4:54 pm
A^2 - B^2 = (A+B)*(A-B)
故
(x^2+8x+17)^2-(2x+8)^2
=[(x^2+8x+17+(2x+8)]*[(x^2+8x+17-(2x+8)]
=(x^2+10x+25)*(x^2+6x+9)
=(x+5)^2*(x+3)^2
=(x+5)^2(x+3)^2
故
(x^2+8x+17)^2-(2x+8)^2
=[(x^2+8x+17+(2x+8)]*[(x^2+8x+17-(2x+8)]
=(x^2+10x+25)*(x^2+6x+9)
=(x+5)^2*(x+3)^2
=(x+5)^2(x+3)^2
2017-11-09 5:56 am
Sol
(x^2+8x+17)^2－(2x+8)^2
=[(x^2+8x+17)－(2x+8)]*[(x^2+8x+17)+(2x+8)]
=(x^2+6x+9)(x^2+10x+25)
=(x+3)^2(x+5)^2
(x^2+8x+17)^2－(2x+8)^2
=[(x^2+8x+17)－(2x+8)]*[(x^2+8x+17)+(2x+8)]
=(x^2+6x+9)(x^2+10x+25)
=(x+3)^2(x+5)^2
收錄日期: 2021-04-24 00:51:37
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20171108170312AAhboLh