因式分解題目2,較多...(20分!!!)

1)k-8k+16=(k-4)^2//

2)9m-4n=(3m+2n)(3m-2n)//

3)Factorize the following polynomials:
A.)x-16=(x-4)(x+4)/
B.)4y-25=(2y-5)(2y+5)//
C.)-49a+1=-(7a+1)(7a-1)//
D.)36u-64v=(6u-8v)(6u+8v)=4(3u-4v)(3u+4v)//
E.)81x^4-4y^4=(9x^2-2y^2)(9x^2+2y^2)//
F.)(6r+3s)-(r-s)=(6r+3s+r-s)(6r+3s-r+s)=(7r-2s)(5r+4s)//
G.)y+4y+4=(y+2)^2//
H.)m-10m+25=(m-5)^2//
I.)64-16p+p=(p-8)^2//
J.)9u+12uv+4v=(3u+2v)^2//
K.)49a+25b^4-70ab=(7a-5b)^2//
L.)32y^4+96xy+72x^4=8(3x^2+2y^2)^2//


2008-07-15 21:52:32 補充：
4)
A.)Factorize 4x²-a². and 625x²+450xy+81y².
Ans:
4x²-a².=(2x-a)(2x+a)
625x²+450xy+81y²=(25x+9y)^2//

B.)Using the result of parts(A),Factorize 4x²+(625x²+450xy+81y²).
=4x^2+(25x+9y)^2
=(2x+25x+9y)(2x-25x-9y)
=(27x+9y)(-23x-9y)
=-9(3x+y)(23x+9y)//

2008-07-15 21:54:33 補充：
5)Factorize the following expressions.
A.)8p²+96p+288=8(p^2+12p+36)=8(p+6)^2//
B.)15m²-100m+60=5(3m^2-20m+12)=5(3m-2)(m-6)//
C.)4(u+v)²+9(u-v)²+12(u²-v²)
=4(u+v)²+9(u-v)²+12(u-v)(u+v)
=[2(u+v)+3(u-v)]^2
=(5u-v)^2//

2008-07-15 21:57:09 補充：
6)
A.)Factorize (x+y)²-(x-y)²=(x+y+x-y)(x+y-x+y)=4xy//
B.)Henze,factorize (4x-6)²-(6-2x)²by putting y+3x-6.
=(4x-6)²-(6-2x)²
=(4x-6+6-2x)(4x-6-6+2x)
=(2x)(6x-12)
=12(x)(x-2)//

7)
A.)Expand (a+1)(3a-8)=3a^2-5a-8//
B.)Using the result of part(a),factorize
3u(u+1)²-5u(u+1)-8u
=u[3(u+1)²-5(u+1)-8]
=u(u+1)(3u-8)//

2008-07-15 21:59:56 補充：
8)
A.)Factorize r²+7r-18=(r+9)(r-2)//
B.)Using the result of part(a),factorize
x²+4xy+4y²+7(x+2y)-18
=(x+2y)^2+7(x+2y)-18
=(x+2y+9)(x+2y-2)//

2008-07-15 21:59:58 補充：
9.)Factoriza the following polynomials.
A.)2a²+10a+12=2(a+5a+6)=2(a+2)(a+3)//
B.)2a²b+10ab+12b=2b(a^2+5a+6)=2b(a+2)(a+3)//
C.)2b(c-3)²-10b(3-c)+12b
=2b[(c-3)²-5(3-c)+6]
=2b(c-3-5)(c-3-1)
=2b(c-8)(c-4)//

1)k²-8k+16
=(k-4)^2

2)9m²-4n²
=(3m)^2 - (2n)^2
=(3m-2n)(3m+2n)

3A.)x²-16=(x+4)(x-4)
B.)4y²-25=(2y+5)(2y-5)
C.)-49a²+1=(1+7a)(1-7a)
D.)36u²-64v²=(6u+8v)(6u-8v)
E.)81x^4-4y^4=(9x^2+2y^2)(9x^2-2y^2)
F.)(6r+3s)²-(r-s)²=(6r+3s+r-s)(6r+3s-r+s)=(7r+2s)(5r+4s)
G.)y²+4y+4=(y+2)^2
H.)m²-10m+25=(m-5)^2
I.)64-16p+p²=(8-p)^2
J.)9u²+12uv+4v²=(3u+2v)^2
K.)49a^4+25b^4-70a²b²=(7a^2-5b^2)^2
L.)32y^4+96x²y²+72x^4=8(2y^2+3x^2)^2

4A)4x²-a²=(2x-a)(2x+a)
625x²+450xy+81y²=(25x+9y)^2
B)4x²-(625x²+450xy+81y²)
=4x²-(25x+9y)^2
=(2x-25x-9y)(2x+25x+9y)
=-9(23x+9y)(3x+y)

5A.)8p²+96p+288=8(p²+12p+36)=8(p+6)^2
B.)15m²-100m+60=5(3m²-20m+12)=5(3m-2)(m-6)
C.)4(u+v)²+9(u-v)²+12(u²-v²)=[2(u+v)+3(u-v)]^2=(5u-v)^2

6A)(x+y)²-(x-y)²=(2y)(2x)=4xy
B)put y=3x-6,
(4x-6)²-(6-2x)²=[x+(3x-6)]^2-[x-(3x-6)]^2
=4x(3x-6)=12x^2-24x

7A)(a+1)(3a-8)=3a^2-5a-8
B)3u(u+1)²-5u(u+1)-8u=u[3(u+1)²-5(u+1)-8]
=u(u+2)(3u-5)

8A)r²+7r-18=(r-2)(r+9)
B)x²+4xy+4y²+7(x+2y)-18
=(x+2y)^2+7(x+2y)-18
=(x+2y-2)(x+2y+9)

9A)2a²+10a+12=2(a+2)(a+3)
B.)2a²b+10ab+12b=2b(a+2)(a+3)
C.)2b(c-3)²-10b(3-c)+12b= 2bc(c-1)

1.(k-4)(k-4)
2.(3m+2n)(3m-2n)

3.唔想計 s0r"
a.(x-4)(x+4)
b.(2y+5)(2y-5)
c.-(7a+1)(7a-1)
d.4(3u+4v)(3u-4v)
e.(9x^2+2y^2)(9x^2-2y^2)
f.唔想計 s0r"
g.(y+2)(y+2)
h.(m-5)(m-5)
i.(8-p)(8-p)
j.(3u+2v)(3u+2v)
k.唔想計 s0r"
l.2(4y^2+6x^2)^2

後邊果d要計""
加油啦!!