math~~~~~~~~~~~~~因式問題一題,請解答

咁會易明d

http://i463.photobucket.com/albums/qq359/stcf1994/maths/a2-b2.jpg
此為a^2-b^2

http://i463.photobucket.com/albums/qq359/stcf1994/maths/ab2.jpg
此為(a+b)^2

http://i463.photobucket.com/albums/qq359/stcf1994/maths/a2b2.jpg
此為a^2+b^2


4x^2+9y^2=/=4x^2+12xy+9y^2(多左個+12xy)
不過a^2+b^2=(a+b)^2-2ab

要解 li 個, 先要識:
identity 恆等式
An equation in x that can be statisfied by any value of x is called an identity.
(可以代入任何數)



1.為何4x^2-9y^2
能夠(2x+3y)(2x-3y)

係一個 identity 恆等式 , f.2 會學:
difference of two squares : (a+b)(a-b) = a^2 - b^2
(a+b)(a-b)
=a(a-b) +b(a-b)
=a^2 -ab +ab -b^2
=a^2 -b^2

a = 2x, b = 3y
你的例題:
(2x+3y)(2x-3y)
= 2x(2x-3y) +3y(2x-3y)
= 4x^2 -6xy +6xy -9y^2
= 4x^2 -9y^2
因為 (a+b)(a-b), ab 有一加一減, 即[-ab +ab] , 所以冇左 ab
你的例子: [見 step 2] 6xy 有一加一減[-6xy +6xy], 所以冇左6xy



2.但4x^2+9y^2
不能(2x+3y)(2x+3y)
變成4x^2+12xy+9y^2

li 個係另一個 identity
The prefect square expression: (a+b)^2 = a^2 +2ab +b^2
(a+b)^2
= (a+b)(a+b)
= a(a+b)+b(a+b)
= a^2 +ab +ab +b^2
= a^2 +2ab +b^2

a = 2x, b = 3y
你的例題:
(2x+3y)(2x+3y)
= 2x(2x+3y) +3y(2x+3y)
= 4x^2 +6xy +6xy +9y^2
= 4x^2 +12xy +9y^2
因為 (a+b)(a+b), ab 有, 即[+ab +ab] , 所以係2ab
你的例子: [見 step 2] 6xy 有兩加[+6xy +6xy], 所以係 2個(6xy), 即12xy



總結
因為 (a+b)(a-b), ab 有一加一減, 即[-ab +ab] , 所以冇左 ab
但 (a+b)(a+b), ab 有兩加冇減, 即[+ab +ab], 所以係 2ab
[(a-b)(a-b) 亦如是` ab 有兩減冇加, 即[-ab -ab], 所以係 -2ab

我係f.2學生, 自己解俾你聽架` 冇copy ` 打左好耐`
再唔明就繼續睇, 睇到明啦` 加油!

Identity:
An equation in x that can be statisfied by any value of x is called an identity.

1. difference of two squares :
(a+b)(a-b) = a^2 - b^2

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


2. The prefect square expression:
A: (a+b)^2 = a^2 +2ab +b^2
B: (a-b)^2 = a^2 -2ab +b^2

A:
(a+b)^2
= (a+b)(a+b)
= a(a+b)+b(a+b)
= a^2 +ab +ab +b^2
= a^2 +2ab +b^2


B:
(a-b)^2
= (a-b)(a-b)
= a(a-b)-b(a-b)
= a^2 -ab -ab +b^2
= a^2 -2ab +b^2


3. Sum and difference of two cubes
A: a^3 +b^3 = (a+b)(a^2 -ab +b^2)
B: a^3 -b^3 = (a-b)(a^2 +ab +b^2)

A:
(a+b)(a^2 -ab +b^2)
= a(a^2 -ab +b^2) +b(a^2 -ab +b^2)
= a^3 -a^2b +ab^2 +a^2b -ab^2 +b^3
= a^3 +b^3


B:
(a-b)(a^2 +ab +b^2)
= a(a^2 +ab +b^2) -b(a^2 +ab +b^2)
= a^3 +a^2b +ab^2 -a^2b -ab^2 -b^3
= a^3 -b^3

2010-01-07 16:02:00 補充：
Identity:
An equation in x that can be statisfied by any value of x is called an identity.
(a+b)(a-b) = a^2 - b^2
(a+b)^2 = a^2 +2ab +b^2
(a-b)^2 = a^2 -2ab +b^2
a^3 +b^3 = (a+b)(a^2 -ab +b^2)
a^3 -b^3 = (a-b)(a^2 +ab +b^2)

2010-01-07 16:02:30 補充：
背左佢地!

同果3條恆待式一樣
1. ( a + b ) ^ 2 = a ^ 2 + 2ab + b ^ 2
2. ( a - b ) ^ 2 = a ^ 2 - 2ab + b ^ 2
3. (a + b) (a - b ) = a ^ 2 - b ^ 2

4x^2 - 9y^2
能夠( 2x + 3y )( 2x - 3y )
就係同第3條一樣.


但係4x^2+9y^2將佢變成
(4x + 9y )^2
就會同第一條一樣..
所以就會變成4x^2+12xy+9y^2啦

背好3條恆等式佢,就唔會再問e個問題架啦..: )
加油!