F.2 math 因式分解`

根據 Yahoo! 知識+ 幾年前的規定，呢度係唔比幫人做功課...

不過，教人做數都仲好似得，所以我系度教你做幾條，其後果D就靠自己了...

初中 Factorization 有分幾種方法，包括：
一、 Grouping terms 及抽 common Factor
二、 用 Identities
三、 用 cross method
由於各方法係根據條數ge類型而使用，所以我會抽幾條有代表性ge數黎教

1) 5x(x + y) - (x + y)
做法：看到兩個一樣的東西時 (這裡的 x + y)，不用多說，肯定係用方法一了
solution: (x + y) (5x - 1)

2) (a + b)^2 + (a + b)b
做法：這裡的common factor 難一點點抽出來。因為 (a + b)^2 其實係 (a + b)(a + b)，所以抽的時候小心點
Further steps: (a + b) [(a + b) + b]
solution: (a + b)(a + 2b)

類似方式題目：Q 13, 14


3) x^2 - 400
做法：這裡冇common factor 可抽。如果看到有「二次方」的物體出現，多數會用到方法二。
以下係幾條中一至三必用的Identities，請小心牢記。
x^2 - y^2 = (x + y)(x - y)
x^2 + 2xy + y^2 = (x + y)^2
x^2 - 2xy + y^2 = (x - y)^2
x^3 + y^3 = (x + y)(x^2 - xy + y^2)
x^3 - y^3 = (x - y)(x^2 + xy + y^2)
Further steps: (x)^2 - (20)^2
solution: (x + 20)(x - 20)

類似方式題目：Q 4 - 10, 15 - 17, 19 - 21

另外有個 cross method ge東西，我唔系度再打一次啦... 我比我曾經答過ge一條題目個link你，自己學習吧..

http://hk.knowledge.yahoo.com/question/question?qid=7008100802140

Hints：如果唔識計，用mouse Highlight 以下題號黎睇下D提示
10) 先排位，再用方法二
13) 先拆開 6(u-2v) ，跟住 grouping terms ，再抽common factor
14) 頭兩項用 identity ，跟住再抽common factor
15) 當2x + 3 係一個數咁做，如果唔係好得，let a = 2x + 3，用完 identity 就會搵到a。代返個答案落去a = 2x + 3就搵到 x
16) 同上
17) 先 factorize 前面括號，搵到答案後睇下用 identity 定係 common factor 再 factorize

如果都係唔識... 你係條問題度話比我聽，我會盡快解決佢

還有... Q11, 12.. 你肯定你冇打錯嗎?

呢個係我另一個有關 factorization ge 題目，自己參考下啦..
http://hk.knowledge.yahoo.com/question/question?qid=7008092301280



2010-08-12 13:22:42 補充：
哪你是否想寫 (p^2)q+24-4p-6pq 和 (6m^2)n+20+32m^2+35n 呢...... ??

2010-08-12 18:03:40 補充：
7.m^2-20m+100
=(m)^2-2(m)(10)+(10)^2
=......
還記得有條 identity 係 x^2 + 2xy + y^2 = (x + y)^2 嗎??

你當 m = x, 10 = y，睇下計唔計到...

2010-08-12 18:04:18 補充：
sorry... 係 x^2 - 2xy + y^2 = (x - y)^2

2010-08-12 18:17:56 補充：
11) Grouping terms 再抽 common Factor
12) 同上

4.x^2-144x^2-12^2(x + 12) (x – 12)5.25x^2-y^25^2 x^2-y^2(5x)^2 – y^2(5x +y)(5x – y)6.36-49n^26^2-7^2n^26^2-7^2n^26^2-(7n)^2(6 + 7n)(6-7n)7.m^2-20m+100  m^2-10m – 10m+100m(m – 10) – 10(m – 10)(m -10)(m-10)(m – 10)^28. 9x^2+24x+16(3x +4)(3x +4)(3x +4)^29.49y^2-28y+4(7y – 2) (7y -2)10.16z^2+81+72z16z^2+72z +81(4z +9)(4z + 9)(4z + 9)^211.(p^2)q+24-4p-6pq.(p^2)q-4p-6pq +24p(pq - 4)-6(pq -4)(pq – 4) (p – 6)12. (56m^2)n+20+32m^2+35n.     (56m^2)n+32m^2+35n + 20      8m^2(7n + 4) +5(7n + 4)      (7n + 4)(8m^2+5)13.u^2-4v^2+6(u-2v)   u^2-4v^2+6(u-2v)   u^2 – (2v)^2 + 6(u– 2v)   (u + 2v)(u-2v) +6(u-2v)    (u – 2v)(u +2v +6)14.9m^2-16n^2-3mk-4nk   9m^2-16n^2-k(3m+4n)   3^2m^2-4^2n^2-k(3m+4n)(3m)^2 – (4n)^2 - k(3m+4n)(3m+ 4n) (3m – 4n) - k(3m+4n)(3m + 4n)(3m – 4n –k)15.(2x+3)^2+4(2x+3)+4     Let k = (2x +3)     k^2 + 4k +4     (k  +2)(k +2)      put k = 2x + 3             (2x + 3 +2) (2x +3 +2)     (x +5) (x +5)     (x +5)^216.(10k+7h)^2-2h(10k+7h)+h^2      Let x =.(10k+7h)^2-2h(10k+7h)+h^2 (10k+7h)     x^2-2hx+h^2     (x – h)(x – h)     Put x =10 k +7h     (10k + 7h – h) (10k+ 7h – h)     (10k +6h)(10k+6h)     2(5k +3h)2(5k+3h)     4(5k + 3h)^217.(16x^2-8xy+y^2)-25(x-1)^2      (4x – y)(4x –y)- 25(x – 1)^2(4x – y)(4x – y)- 5^2(x – 1)^2(4x – y)^2- (5x – 5)^2(4x – y  +x – 5) (4x –y  -x + 5)(5x – y  – 5) (3x – y+ 5)18.18p^2-2q^2+12q-18      2(9p^2- q^2 + q –9)    2[9p^2- (q-3)(q-3)]    2[(3p)^2- (q - 3)^2]   2[3p +q – 3][3p-q+3]19. x^2+12xy+36y^2     (x +6y)(x+6y)      (x +6y)^220. p^2+121q^2+22pq     p^2+22pq+121q^2    (p +11q) (p +11q)    (p + 11q)^221.40mn+16m^2+25n^216m^2 +40mn + 25n^2(4m + 5n)(4m + 5n)

2010-08-16 12:44:17 補充：
You had better do your homework and check with my answer.

這裏可以幫到你
http://yahoain.v50.host11.net/yahoo.com.hk/hk/auction/178987536