Factorize the following expressions.
1. 9x^2 - 6xy + y^2 - (2xy)^2
Maths!!!
2008-11-19 2:20 am
回答 (2)
2008-12-02 5:21 am
✔ 最佳答案
1. 9x2 - 6xy + y2 - (2xy)2
Using a bracket to seperate them
= (9x2 - 6xy + y2) - (2xy)2
Using the identity of (a - b)2 ≡ a2 - 2ab + b2 to factorize the first part
= (3x - y)2 - (2xy)2
Using the identity of a2 - b2 ≡ (a + b)(a - b)
= [(3x - y) + 2xy][(3x - y) - 2xy]
= (3x + 2xy - y)(3x - 2xy - y)
參考: myself
2008-11-19 3:23 am
1.
9x^2 - 6xy + y^2 - (2xy)^2
=9x² - 6xy + y² - (2xy)²
=(3x)² -2(3x)(y)+(y)² - (2xy)²
=(3x-y)² -(2xy)²....................................a²-2ab+b²=(a-b)²
=(3x-y+2xy)(3x-y-2xy)..........................a²-b²=(a-b)(a+b)
9x^2 - 6xy + y^2 - (2xy)^2
=9x² - 6xy + y² - (2xy)²
=(3x)² -2(3x)(y)+(y)² - (2xy)²
=(3x-y)² -(2xy)²....................................a²-2ab+b²=(a-b)²
=(3x-y+2xy)(3x-y-2xy)..........................a²-b²=(a-b)(a+b)
參考: 會考數學拿c既人~
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