F.2數學題(15分)

hiutung

2009-04-16 7:18 am

F.2數學題,一共9題...希望大家教教我.^^.(唔該俾埋steps)...好急架!!

要用恆等公式(identities)!!

1.)Factorize x^4-1

2.)Factorize a^4-16

3.)Factorize x^2-2x+1-4y^2

4.)Factorize a^2-2ab+b^2-a+b

5.)Simplify (a+b)^2-(a-b)^2

6.)9-a^2-b^2+2ab=?

7.)Factorize x^2-y^2+2x+1

8.)x^2-y^2-x+y

9.)x^2-(y-z)^2

回答 (1)

用戶2053

2009-04-16 7:45 am

✔ 最佳答案

1.)Factorize x^4-1
= (x^2)^2 - 1
=(x^2 - 1)(x^2 + 1)
= (x-1)(x+1)(x^2 + 1)
2.)Factorize a^4-16
= (a^2)^2 - 4^2
= (a^2 - 4)(a^2 + 4)
= (a-2)(a+2)(a^2 + 4)
3.)Factorize x^2-2x+1-4y^2
= (x^2-2x+1) - 4y^2
= (x - 1)^2 - (2y)^2
= (x-2y-1)(x+2y-1)
4.)Factorize a^2-2ab+b^2-a+b
= (a^2 - 2ab + b^2) - (a - b)
= (a-b)^2 - (a-b)
= (a-b)(a-b-1)
5.)Simplify (a+b)^2-(a-b)^2
= [(a+b)-(a-b)] [(a+b)+(a-b)]
= 2b * 2a
= 4ab
6.)9-a^2-b^2+2ab=?

= 9 - (a^2 - 2ab + b^2)
= 3^2 - (a-b)^2
= (3-a+b) (3+a-b)
7.)Factorize x^2-y^2+2x+1
= (x^2+2x+1) - y^2
= (x+1)^2 - y^2
= (x+y-1)(x-y+1)
8.)x^2-y^2-x+y
= (x-y)(x+y) - (x-y)
= (x-y)(x+y-1)
9.)x^2-(y-z)^2
= (x-y+z)(x+y-z)

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2009-04-15 23:48:03 補充：
For 7). the answer should be (x-y+1)(x+y+1)

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