Identities and Factorization
1. 4a^2b^2 - (b^2+6b+9)
2. 9x^2 - 6xy +y^2 - 4x^2y^2
3. a^2 - b^2 + 2a^2b - 2ab^2
急!F.2 MATHS 問題20分
2011-09-21 1:51 am
回答 (2)
2011-09-21 2:15 am
✔ 最佳答案
1. 4a^2b^2 - (b^2+6b+9)= (2ab)^2 - (b+3)^2
= (2ab + b +3)(2ab - b - 3)
2. 9x^2 - 6xy +y^2 - 4x^2y^2
= (3x - y)^2 - (2xy)^2
= (3x - y + 2xy)(3x - y - 2xy)
3. a^2 - b^2 + 2a^2b - 2ab^2
= (a+b)(a-b) + 2ab(a-b)
= (a-b)(a+b+2ab)
2011-09-21 2:21 am
1. 4a^2b^2 - (b^2+6b+9)
=(2ab)^2 - (b+3)^2
=<2ab+(b+3)><2ab-(b+3)>
=(2ab+b+3)(2ab-b-3)
2. 9x^2 - 6xy +y^2 - 4x^2y^2
=(9x^2-6xy+y^2) - 4x^2y^2
=(3x+y)^2 - (2xy)^2
=(3x+y+2xy)(3x+y-2xy)
3. a^2 - b^2 + 2a^2b - 2ab^2
=(a+b)(a-b) + 2ab(a-b)
=(a-b)(a+b+2ab)
2011-09-20 18:22:57 補充：
2. the third step should be (3x-y)^2
and the answer should be (3x-y+2xy)(3x-y-2xy)
=(2ab)^2 - (b+3)^2
=<2ab+(b+3)><2ab-(b+3)>
=(2ab+b+3)(2ab-b-3)
2. 9x^2 - 6xy +y^2 - 4x^2y^2
=(9x^2-6xy+y^2) - 4x^2y^2
=(3x+y)^2 - (2xy)^2
=(3x+y+2xy)(3x+y-2xy)
3. a^2 - b^2 + 2a^2b - 2ab^2
=(a+b)(a-b) + 2ab(a-b)
=(a-b)(a+b+2ab)
2011-09-20 18:22:57 補充：
2. the third step should be (3x-y)^2
and the answer should be (3x-y+2xy)(3x-y-2xy)
參考: textbook
收錄日期: 2021-04-20 11:31:24
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