help me .f.2 mathss!!!!!! improtant , 20pts!!!~~

1) 6ac-bd-6ad+bc
= 6ac + bc – 6ad – bd
= c(6a + b) – d(6a + d)
= (c + d)(6a + b)

2) 5b2 +6cd+3bd+10bc
= 5b2 + 10bc + 3bd + 6cd
= 5b(b + 2c) + 3d(b + 2c)
= (5b + 3d)(b + 2c)

3) 2a^2-9bc-6ab+3ac
= 2a^2 – 6ab + 3ac – 9bc
= 2a(a – 3b) + 3c(a – 3b)
= (2a + 3c)(a – 3b)

4) 14rx-40sy+35sx+16ry
這題不可以分解
但若改為14rx-40sy-35sx+16ry
則變為
14rx-40sy-35sx+16ry
= 14rx – 35sx + 16ry – 40sy
= 7x(2r – 5s) + 8y(2r – 5s)
= (7x + 8y)(2r – 5s)

5) r^2-rs-rt+st
= r(r-s) – t(r-s)
= (r-t)(r-s)

6) mh-mk+h^2-hk
= m(h-k)+h(h-k)
= (m+h)(h-k)

7) 6g-g^2+6h-gh
= g(6-g) + h(6-g)
= (g+h)(6-g)

8) x^2y+ax+bxy+ab
= x^2y + bxy + ax + ab
= xy(x+b)+a(x+b)
= (xy + a)(x + b)

9) y^3 +y^2+y+1
= y^2(y+1)+(y+1)
= (y^2+1)(y+1)

10)9x^3-5x^2-18x+10
= x^2(9x-5)-2(9x-5)
=(x^2-2)(9x-5)

11)2+3a-14a^2-21a^3
= (2+3a) – 7a^2(2+3a)
= (2+3a)(1-7a^2)

12)4ab-6ab^2-2+3b
= 2ab(2-3b)-(2-3b)
= (2ab – 1)(2 – 3b)

13)x^3+yz+xy+x^2z
= x^3 + x^2z + yz + xy
= x^2(x+z) + y(x+z)
= (x^2 + y)(x + z)

14)p^3+a^2p+bp^2+a^2b
= p(p^2+a^2) + b(p^2 + a^2)
= (p + b)(p2 + a2)

15)p^2r^2+p^2s^2+q^2s^2+q^2r^2
=p^2(r^2+s^2)+q^2(s^2+r^2)
=p^2(r^2+s^2)+q^2(r^2+s^2)
=(p^2 + q^2)(r^2+s^2)

16)b+a^3-a+ba^2
不可分解

除了不可分解外，全部做齊了。

2006-11-22 19:54:05 補充：
第一位朋友第四題是錯的，若式是正確是不可分解的

Q1
6ac-bd-6ad+bc
=6a(c-d)-b(d-c)
=6a(c-d)+b(c-d)
=(c-d)(6a+b)

Q2
5b²+6cd+3bd+10bc
=5b(b+2c)+3d(2c+b)
=5b(b+2c)+3d(b+2c)
=(b+2c)(5b+3d)
When (2c+b) changes into (b+2c), it will not be (-)

Q3
2a²-9bc-6ab+3ac
=2a(a-3b)-3c(3b-a)
=2a(a-3b)+3c(a-3b)
=(a-3b)(2a+3c)

Q4
14rx-40sy+35sx-16ry
=7x(2r+5s)-8y(5s+2r)
=(2r+5s)(7x-8y)
The -16ry may be not correct, is it +16ry?

Q5
r²-rs-rt+st
=r(r-s)-t(r-s)
=(r-s)(r-t)

Q6
mh-mk+h²-hk
=m(h-k)+h(h-k)
=(h-k)(m+h)

Q7
6g-g²+6h-gh
=6(g+h)-g(g+h)
=(g+h)(6-g)

Q8
x²y+ax+bxy+ab
=x(xy+a)+b(xy+a)
=(xy+a)(x+b)

Q9
y³+y²+y+1
=y²(y+1)+(y+1)
=(y+1)(y²+1)
When there is no number, a real number 1 appears.

Q10
9x³-5x²-18x+10
=9x(x²-2)-5(x²-2)
=(x²-2)(9x-5)

Q11
2+3a-14a²-21a³
=(2+3a)-7a²(2+3a)
=(a+3a)(1-7a²)

Q12
4ab-6ab²-2+3b
=2ab(2-3b)-(2-3b)
=(2-3b)(2ab-1)

Q13
x³+yz+xy+x²z
=x²(x+z)+y(z+x)
=(x+z)(x²+y)

Q14
p³+a²p+bp²+a²b
=p²(p+b)+a²(p+b)
=(p+b)(p²+a²)

Q15
p²r²+p²s²+q²s²+q²r²
=p²(r²+s²)+q²(s²+r²)
=(r²+s²)(p²+q²)

Q16
b+a³+a+ba²
=a(a²+1)+b(1+a²)
=(a²+1)(a+b)
Is the -a wrong?

1)6ac-bd-6ad+bc
=6ac-6ad-bd+bc
=6a(c-d)+b(-d+c)
=(6a+b)(c-d)
------------------------------------------------------------------------------------------------------
2)5b² ²+6cd+3bd+10bc
=5b^4+10bc+6cd+3bd
=5b(b^3+2c)+3d(2c+b)
=無解
-------------------------------------------------------------------------------------------------------
3)2a²-9bc-6ab+3ac
=2a²-6ab-9bc+3ac
=2a(a-3b)+3c(-3b+a)
=(2a+3c)(a-3b)
-------------------------------------------------------------------------------------------------------
4)14rx-40sy+35sx+16ry
=14rx+16ry-40sy+35sx
=2r(7x+8y)+5s(-8y+7x)
=無解
-------------------------------------------------------------------------------------------------------
5)r²-rs-rt+st
=r(r-s)+t(-r+s)
=r(r-s)-t(r-s)
=(r-t)(r-s)
-------------------------------------------------------------------------------------------------------
6)mh-mk+h²-hk
=m(h-k)+h(h-k)
=(m+h)(h-k)
-------------------------------------------------------------------------------------------------------
7)6g-g²+6h-gh
=6g+6h-g²-gh
=6(g+h)+g(-g-h)
=6(g+h)-g(g+h)
=(6-g)(g+h)
-------------------------------------------------------------------------------------------------------
8)x²y+ax+bxy+ab
=x²y+bxy+ax+ab
=xy(x+b)+a(x+b)
=(xy+a)(x+b)
-------------------------------------------------------------------------------------------------------
9)y^3 +y²+y+1
=y²(y+1)+(y+1)
=(y²+1)(y+1)
-------------------------------------------------------------------------------------------------------
10)9x^3-5x²-18x+10
=9x^3-18x-5x²+10
=9x(x²-2)+5(-x²+2)
=9x(x²-2)-5(x²-2)
=(9x-5)(x²-2)
-------------------------------------------------------------------------------------------------------
11)2+3a-14a²-21a^3
=(2+3a)+7a²(2+3a)
=(1+7a²)(2+3a)
-------------------------------------------------------------------------------------------------------
12)4ab-6ab²-2+3b
=2ab(2-3b)-(2-3b)
=(2ab-1)(2-3b)
-------------------------------------------------------------------------------------------------------
13)x^3+yz+xy+x²z
=x^3+x²z+yz+xy
=x²(x+z)+y(z+x)
=(x²+y)(x+z)
-------------------------------------------------------------------------------------------------------
14)p^3+a²p+bp²+a²b
=p^3+bp²+a²p+a²b
=p²(p+b)+a²(p+b)
=(p²+a²)(p+b)
-------------------------------------------------------------------------------------------------------
15)p²r²+p²s²+q²s²+q²r²
=p²(r²+s²)+q²(s²+r²)
=(p²+q²)(r²+s²)
-------------------------------------------------------------------------------------------------------
16)b+a^3-a+ba²
=b+ba²+a^3-a
=b(1+a²)+a(a²-1)
=無解

2006-11-23 17:28:21 補充：
點解上面的人全部都當5b既2次方既2次方=5b既2次方?Q.2

Q1
6ac-bd-6ad+bc
=6a(c-d)-b(d-c)
=6a(c-d)+b(c-d)
=(c-d)(6a+b)

Q2
5b²+6cd+3bd+10bc
=5b(b+2c)+3d(2c+b)
=5b(b+2c)+3d(b+2c)
=(b+2c)(5b+3d)
When (2c+b) changes into (b+2c), it will not be (-)

Q3
2a²-9bc-6ab+3ac
=2a(a-3b)-3c(3b-a)
=2a(a-3b)+3c(a-3b)
=(a-3b)(2a+3c)

Q4
14rx-40sy+35sx-16ry
=7x(2r+5s)-8y(5s+2r)
=(2r+5s)(7x-8y)
The -16ry may be not correct, is it +16ry?

Q5
r²-rs-rt+st
=r(r-s)-t(r-s)
=(r-s)(r-t)

Q6
mh-mk+h²-hk
=m(h-k)+h(h-k)
=(h-k)(m+h)

Q7
6g-g²+6h-gh
=6(g+h)-g(g+h)
=(g+h)(6-g)

Q8
x²y+ax+bxy+ab
=x(xy+a)+b(xy+a)
=(xy+a)(x+b)

Q9
y³+y²+y+1
=y²(y+1)+(y+1)
=(y+1)(y²+1)
When there is no number, a real number 1 appears.

Q10
9x³-5x²-18x+10
=9x(x²-2)-5(x²-2)
=(x²-2)(9x-5)

Q11
2+3a-14a²-21a³
=(2+3a)-7a²(2+3a)
=(a+3a)(1-7a²)

Q12
4ab-6ab²-2+3b
=2ab(2-3b)-(2-3b)
=(2-3b)(2ab-1)

Q13
x³+yz+xy+x²z
=x²(x+z)+y(z+x)
=(x+z)(x²+y)

Q14
p³+a²p+bp²+a²b
=p²(p+b)+a²(p+b)
=(p+b)(p²+a²)

Q15
p²r²+p²s²+q²s²+q²r²
=p²(r²+s²)+q²(s²+r²)
=(r²+s²)(p²+q²)

Q16
b+a³+a+ba²
=a(a²+1)+b(1+a²)
=(a²+1)(a+b)
Is the -a wrong? +a?

1) 6a(c-d)+b(-d+c) / c(6a+b)+d(b-6a)
2) I DONT KNOW
3) I DONT KNOW
4) 2r(7x+8y)+5s(-8y+7x) / 7x(2r+5s)+8y(-5s+2r)
5) r(r-s-t)+st / r(r-s)+t(-r+s) / r(r-t)+s(-r+t)
6) h(m+h-k)-mk / h(m+h)-k(m+h) / m(h-k)+h(h-k)
7) g(6-g-h)+6h / g(6-g)+h(6-g) / g(g-h)+6(g+h)
8) x(xy+a+by)+ab / x(xy+a)+b(xy+a) / xy(x+b)+a(x+b)
9) y(y既2次方+y+1)+1
10)I DONT KNOW
11)I DONT KNOW
12)I DONT KNOW
13)x(x既2次方+y+xz)+yz / x(x既2次方+xz)+y(z+x) / x(x既2次方+y)+z(y+x既2次方)
14)I DONT KNOW
15)I DONT KNOW
16)I DONT KNOW
DONT KNOW 係因為條問題唔清楚你想講既2次方係成個數定某一個字:)

1) 6ac-bd-6ad+bc = 6a(c-d)+b(c-d) = (6a+b)(c-d)

2) 5b既２次方既２次方+6cd+3bd+10bc = 5b(b+2c)+3d(b+2c) = (5b+3d)(b+2c)

3) 2a既２次方-9bc-6ab+3ac = 2a(a-3b)+3c(a-3b) = (2a+3c)(a-3b)

4) 14rx-40sy+35sx+16ry =7x(2r+5s)-8y(2r+5s) = (7x-8y)(2r+5s)

5) r既２次方-rs-rt+st = r(r-t)-s(r-t) = (r-s)(r-t)

6) mh-mk+h既２次方-hk = m(h-k)+h(h-k) = (m+h)(h-k)

7) 6g-g既２次方+6h-gh = 6(g+h) - g(g-h) = (6-g)(g-h)

8) x既２次方y+ax+bxy+ab = xy(x+b) +a(x+b) = (xy+a)(x+b)

9) y既3次方+y既２次方+y+1 = y既２次方(y+1) + (y+1) = (y既２次方+1)(y+1)

10)9x既3次方-5x既２次方-18x+10 = 9x(x既２次方-2) - 5(x既２次方-2) = (9x-5)(x既２次方-2)

11)2+3a-14a既２次方-21a既3次方 = (2+3a) - 7a既２次方(2+3a) = (2+3a)(1-7a既２次方)

12)4ab-6ab既２次方-2+3b = 2ab(2-3b)-(2-3b) = (2ab-1)(2-3b)

13)x既3次方+yz+xy+x既２次方z = x既２次方(x+z)+y(x+z) = (x既２次方+y)(x+z)

14)p既3次方+a既２次方p+bp既２次方+a既２次方b = p既２次方(p+b)+a既２次方(p+b) = (p既２次方+a既２次方)(p+b)

15)p既２次方r既２次方+p既２次方s既２次方+q既２次方s既２次方+q既２次方r既２次方 = r既２次方(p既２次方+p既２次方) + s既２次方(p既２次方+p既２次方) = (r既２次方 + s既２次方)(p既２次方+p既２次方)

16)b+a既3次方-a+ba既２次方 = b(1+ a既２次方)+a(1+ a既２次方) = (b+a)(1+ a既２次方)