Expand the following expressions. (Use Identity)
1. (x+y+z)(x+y-z)
2. (a-b+c)(a+b-c)
Plz show steps
Form 2 Maths (Identity)
2007-01-03 5:30 am
回答 (4)
2007-01-03 5:34 am
✔ 最佳答案
1. (x+y+z)(x+y-z)(x+y+z)(x+y-z)
= [(x+y)+z] [(x+y)-z]
= (x+y)² - z² 【Using identity a²-b²=(a-b)(a+b)】
= x² + 2xy + y² - z² 【Using identity (a+b)²=a²+2ab+b²】
===========================================
2. (a-b+c)(a+b-c)
(a-b+c)(a+b-c)
= [a-(b-c)] [a+(b-c)]
= a² - (b-c)² 【Using identity a²-b²=(a-b)(a+b)】
= a² - (b² - 2bc + c²) 【Using identity (a-b)²=a²-2ab+b²】
= a² - b² + 2bc - c²
= a² - b² - c² + 2bc
2007-01-03 5:40 am
1. (x+y+z)(x+y-z)
=x^2 + xy -xz + yx + y^2 -yz + zx + zy - z^2
=x^2 + 2xy + y^2 - z^2
2. (a-b+c)(a+b-c)
=a^2 + ab - ac - ba - b^2 + bc + ca + cb - c^2
=a^2 + 2bc - b^2 - c^2
=x^2 + xy -xz + yx + y^2 -yz + zx + zy - z^2
=x^2 + 2xy + y^2 - z^2
2. (a-b+c)(a+b-c)
=a^2 + ab - ac - ba - b^2 + bc + ca + cb - c^2
=a^2 + 2bc - b^2 - c^2
2007-01-03 5:39 am
1. =(x+y)^2 - z^2 = x^2 +2xy +y^2 -z^2
2. = [a-(b-c)][a+(b-c)] = a^2 -(b-c)^2 =a^2 - (b^2 -2bc +c^2) = a^2-b^2-c^2 +2bc
2. = [a-(b-c)][a+(b-c)] = a^2 -(b-c)^2 =a^2 - (b^2 -2bc +c^2) = a^2-b^2-c^2 +2bc
2007-01-03 5:37 am
1. (x+y+z)(x+y-z)
= x^2+xy-xz+xy+y^2-yz+xz+yz-z^2
=x^2+2xy+y^2-z^2
2. (a-b+c)(a+b-c)
=a^2+ab-ac-ab-b^2+bc+ac+bc-c^2
=a^2-b^2+2bc-c^2
= x^2+xy-xz+xy+y^2-yz+xz+yz-z^2
=x^2+2xy+y^2-z^2
2. (a-b+c)(a+b-c)
=a^2+ab-ac-ab-b^2+bc+ac+bc-c^2
=a^2-b^2+2bc-c^2
收錄日期: 2021-04-12 21:59:58
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070102000051KK05188