fORM3 MATHS 請教!!!!

oalylok

(a-b) 2次方  - (a+b)2次方 =?


唔該!!!!!!

oalylok

唔4該呀

凸唯而出

1.a^2 - 2ab + b^2
2.a^2 +2ab + b^2
小心唔好錯

小洋少

a+b a-b 2次好似公式黎

低低…

(a-b)²-(a+b)²
=(a-b)(a-b)-(a+b)(a+b)
=(a²-2ab+b²)-(a²+2ab+b²)
=a²-2ab+b²-a²-2ab-b²
= -4ab

========
恆等式
(a+b)²
=(a²+2ab+b²)
(a-b)²
=(a²-2ab+b²)
a²-b²
=(a=b)(a-b)

oalylok

中間有個減號.....

oalylok

低低… 發表於 11-9-20 10:28 PM
(a-b)²-(a+b)²
=(a-b)(a-b)-(a+b)(a+b)
=(a²-2ab+b²)-(a²+2ab+b²)

我都係計到咁
但個ans 係 (a-b+a+b) (a-b-a+b)...

king266

(a-b)^2  - (a+b)^2 = ?
你應該學過一條式係 (a+b) * (a-b)  =  a^2 - b^2
套返落呢題...即係
(a-b)^2  - (a+b)^2 = [(a-b) + (a+b)] * [(a-b) - (a+b)]
                            = (a - b + a + b) * (a - b - a - b)
                            = (2a) * (-2b)
                            = -4ab

wyz1301c2920

oalylok 發表於 11-9-20 10:32 PM
我都係計到咁
但個ans 係 (a-b+a+b) (a-b-a+b)...

你係咪睇錯左

低低…

oalylok 發表於 11-9-20 10:32 PM
我都係計到咁
但個ans 係 (a-b+a+b) (a-b-a+b)...

(a-b)²-(a+b)²
題目↑
=(a-b)(a-b)-(a+b)(a+b)
(a-b)² = (a+b)(a+b) 純展開
=(a²-2ab+b²)-(a²+2ab+b²)
恆等式 (a+b)² (a-b)²
=a²-2ab+b²-a²-2ab-b²
減號後的符號要相反 e.g : (x+y) - (x-y)  =  x+y - x+y
= -4ab
答案純加減

oalylok

唔該各位...
問多題

(2x-y)² - (x+2y)²
=(2x² + y² - 2xy ) - ( x² + 2y² + 2xy )
=2x² + y² - 2xy  - x² - 2y² - 2xy
=x² - y² - 4xy  

???我岩唔岩

oalylok

或者個題目係叫Factorize ..有冇關係?

wyz1301c2920

(2x-y)² - (x+2y)²
=(4x²-4xy+y²)-(x²+4xy+4y²)
=4x²-4xy+y²-x²-4xy-4y²
=4x²-x²+y²-4y²-4xy-4xy
=3x²-3y²-8xy
唔知有冇計錯

小洋少

(2x-y)² - (x+2y)²
=(2x² + y² - 2xy )

2x²?? 4x²??

king266

oalylok 發表於 11-9-20 10:41 PM
唔該各位...
問多題

(2x-y)² - (x+2y)²
=(2x² + y² - 2xy ) - ( x² + 2y² + 2xy )
=2x² + y² - 2xy  - x² - 2y² - 2xy
=x² - y² - 4xy  

bold左既應該係 4x² 同 4y²
因為二次方既係 2x 同 2y...除左個unknown, 個 coeff 都要square埋
斜體既應該係 4xy
要記住條式係
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²

ANS:
(2x-y)² - (x+2y)²
= (4x² - 4xy + y²) - (x² + 4xy + 4y²)
=  4x² - 4xy + y² - x² - 4xy - 4y²
= 3x² - 8xy - 3y²

另一方法
(2x-y)² - (x+2y)²
= [(2x-y) + (x+2y)] * [(2x-y) - (x+2y)]
= (2x - y + x + 2y) * (2x - y - x - 2y)
= (3x + y) * (x - 3y)  [有d老師可能要求用呢行做答案就ok]
= 3x² - 8xy - 3y²

俊??

(2x-y)² - (x+2y)²
=(4x^2-4xy+y^2)-(x^2+4xy+4y^2)
=3x^2-8xy-3y^2
=(3x+y)(x-3y)??

wyz1301c2920

4x²
(2x-y)² - (x+2y)²
=[(2x)²-2(2x)(y)+y²]-[(2x)²+2(2x)(y)+y²]

低低…

俊?? 發表於 11-9-20 10:50 PM
(2x-y)² - (x+2y)²
=(4x^2-4xy+y^2)-(x^2+4xy+4y^2)
=3x^2-8xy-3y^2

5點黎;@
y²-4y² = -3y²

oalylok

ok...原來我誤會左...唔該晒

問多題-.-

25m² - 36n² - 5m - 6n
= 5m(5m -1 ) - 6n (+6n -1 )

之後應該點..唔該..

wyz1301c2920

俊?? 發表於 11-9-20 10:50 PM
(2x-y)² - (x+2y)²
=(4x^2-4xy+y^2)-(x^2+4xy+4y^2)
=3x^2-8xy-3y^2

(2x-y)² - (x+2y)²
=(4x^2-4xy+y^2)-(x^2+4xy+4y^2)
=3x^2+8xy+5y^2
=(3x+y)(x+5y)??

由第三行開始錯了
我估,應該係你正負號唔岩