數學一問！

1.
8a^2-38a+35
=(2a-7)(4a-5)

2.
20-7a-6a^2
=(4-3a)(5+2a)

3.
(a+b)^3-8(a-b)^3
=(a+b)^3-[2(a-b)^3]
=[(a+b)-(2a-2b)][(a+b)^2+(a+b)(2a-2b)+(2a-2b)^2]
=(3b-a)(a^2+2ab+b^2+a^2+b^2+2a^2-2ab+2ab-2b^2+4a^2-8ab+4b^2)
=(3b-a)(8a^2-6ab+4b^2)
=2(3b-a)(4a^2-3ab+2b^2)

4a.因式分解
a^2-2ab+b^2
=(a-b)^2
4b.由此化簡
a^2-2a(a+1)+(a+1)^2
=[a-(a+1)]^2
=(-1)^2=1

5a.因式分解
a^3-8
=a^3-2^3
=(a-2)(a^2+2a+4)

5b.由此因式分解
a^3+2a-12
=a^3-8+(2a-4)
=(a-2)(a^2+2a+4)+2(a-2)
=(a-2)(a^2+2a+4-2)
=(a-2)(a^2+2a+2)

6. 已知以下一組數據：
a/2，4a/5，6a/7，a/3，7a/6
求當中位數是8時a的值。
a/3 < a/2 < 4a/5 < 6a/7 < 7a/6
4a/5=8
a=10

1 ) 8a^2-38a+35
=(2a-7)(4a-5)

2 ) 20-7a-6a^2
=(5+2a)(4-3a)

3 ) (a+b)^3-8(a-b)^3
=(a+b)^3-[2(a-b)]^3
=[(a+b)-2(a-b)]{(a+b)^2-2(a+b)(a-b)+[2(a-b)]^2}
=(a+b-2a+2b)[(a^2+2ab+b^2)-(2a^2-2b^2)+(4a^2-8ab+4b^2)]
=(3b-a)(3a^2-6ab+7b^2)

4a) a^2-2ab+b^2
=(a-b)^2
b) a^2-2a(a+1)+(a+1)^2
=[a-(a+1)]^2
=(-1)^2
=1

5a) a^3-8
=(a-2)(a^2+2a+4)
b) a^3+2a-12
=(a^3-8)+(2a-4)
=(a-2)(a^2+2a+4)+2(a-2)
=(a-2)(a^2+2a+6)

6 ) Given:
(a/2+4a/5+6a/7+a/3+7a/6)/5=8
a/2+4a/5+6a/7+a/3+7a/6=40 (L.C.M. of 2, 5, 7, 3 and 6 is 210)
210(a/2+4a/5+6a/7+a/3+7a/6)=8400
105a+168a+180a+140a+245a=8400
838a=8400
419a=4200
a=4200/419
a=10+10/419

2007-08-22 11:20:07 補充：
Sorry，我睇錯左第６題。Given the medium number is 8.Substuting any value be the medium number.a/2=8,a=16(&gt;0)4a/5=8,a=10(&gt;0)6a/7=8,a=28/3(&gt;0)a/3=8,a=24(&gt;0)7a/6=8,a=48/7(&gt;0)Therefore,if the medium number&gt;0,all values&gt;0.So,a/3<a</a>

1. (4a-5)(2a-7)
2. (2a+5)(4-3a)
3.(2b)[(a+b)^2+(a+b)(a-b)+(a-b)^2]
4a. (a-b)^2
4b. 1
5a. (a-2)(a^2+2a+4)
5b. (a-2)(a^2+2a+6)
6.a/3 &lt; a/2 &lt; 4a/5 &lt; 6a/7 &lt; 7a/6

8a^2-38a+35=(2a-7)(4a-5)

20-7a-6a^2= -6a^2-7a+20=-(6a^2+7a-20)=-(3a-5)(a+2)

3. (a+b)^3-8(a-b)^3
=a^3+3a^2b+3ab^2+b^3-8a^3+24a^2b-24ab^2+8b^3
=-7a^3+27a^2b+21ab^2+9b^3
=

a^2-2ab+b^2=(a-b)^2

a^2-2a(a+1)+(a+1)^2=(a-(a+1)^2=1//

a^3-8=a^3-2^3=(a-2)(a^2+2a+4)

a^3+2a-12=...................

a/2+4a/5+6a/7+a/3+7a/6=128a/35

(128a/35)/5=8
a=10.9375//

1. (4a-5)(2a-7)
2. (2a+5)(4-3a)
3.(2b)[(a+b)^2+(a+b)(a-b)+(a-b)^2]
4a. (a-b)^2
4b. 1
5a. (a-2)(a^2+2a+4)
5b. (a-2)(a^2+2a+6)
6.因為 a/3 &lt; a/2 &lt; 4a/5 &lt; 6a/7 &lt; 7a/6

4a/5 = 8
a= 10