急!!!因式分解難搞題目

Questions and Answers :

Factorize the following expressions.

1. 3a^2-27
= 3 (a^2-9)
= 3 (a-3)(a+3) #

2. mc^2-md^2
= m (c^2-d^2)
= m (c+d)(c-d) #

3. (a+b)^2-c^2
= [ (a+b)-c ] [ (a+b)+c ]
= (a+b-c)(a+b+c) #

4. 4x^2-(x-y)^2
= (2x)^2 - (x-y) ^2
= [ 2x-(x-y) ] [ 2x+(x-y) ]
= (x+y)(3x-y) #

5. 18b^2-8c^2
= 2 (9b^2-4c^2)
= 2 [ (3b)^2 - (2c)^2 ]
= 2 (3b-2c)(3b+2c) #

6.3nk^2-3n
= 3n (k^2-1)
= 3n (k^2-1^2)
= 3n (k-1)(k+1) #

7.(p-3)^2-49
= (p-3)^2- 7^2
= [ (p-3)-7 ] [ (p-3) +7 ]
= (p-10)(p+4) #

8.(2x-3y)^2-(4x-y)^2
= [ (2x-3y)-(4x-y) ] [ (2x-3y)+(4x-y) ]
= (-2x-4y) (6x-4y)
= -2 (x+y) (2) (3x-2y)
= -4 (x+y) (3x-2y) #

9. 4a^2+16a+16
= 4 (a^2+4a+4)
= 4 (a+2)^2 #

10. 18c^2+12cd+2d^2
= 2 (9c^2+6cd+d^2)
= 2 [ (3c)^2 + 2(3c)(d) + (d)^2 ]
= 2 (3c+d)^2 #

1.
3a^2-27
=3(a^2-9)
=3(a-3)(a+3)

2.
mc^2-md^2
=m(c^2-d^2)
=m(c+d)(c-d)

3.
(a+b)^2-c^2
=(a+b-c)(a+b+c)

4.
4x^2-(x-y)^2
=[2x-(x-y)][2x+(x+y)]
=(x-y)(3x+y)

5.
18b^2-8c^2
=2(9b^2-4c^2)
=2(3b-2c)(3b+2c)

6.
3nk^2-3n
=3n(k^2-1)
=3n(k-1)(k+1)

7.
(p-3)^2-49
=[(p-3)-7][(p-3)+7]
=(p-10)(p+4)

8.
(2x-3y)^2-(4x-y)^2
=[(2x-3y)-(4x-y)][(2x-3y)+(4x-y)]
=(-2x-2y)(6x-4y)
=-2(x+y)(2)(3x-2y)
=-4(x+y)(3x-2y)

9.
4a^2+16a+16
=4(a^2+4a+4)
=4(a+2)^2

10.
18c^2+12cd+2d^2
=2(9c^2+6cd+d^2)
=2(3c+d)^2

1.3(a-3)(a+3)
2.m(c-d)(c-d)
3.(a+b-c)(a+b+c)
4.(3x-1)(x+y)
5.2(3b+2c)(3b-2c)
6.3n(k-1)(k+1)
7.(p-10)(p+4)
8.-2(2x+3y)(3x-2y)
9.4(a+2)^2
10.2(3c+d)^2

1. 3a^2-27
3(a^2-9)

2. mc^2-md^2
m(c^2-d^2)
m(c+d)(c-d)

3. (a+b)^2-c^2
(a+b+c)(a+b-c)

4. 4x^2-(x-y)^2
(2x)^2-(x-y)^2
(2x+x-y)(2x-(x-y))
(3x-y)(x+y)

5. 18b^2-8c^2
2(9b^2-4c^2)
2((3b)^2-(2c)^2)
2(3b+2c)(3b-2c)

6.3nk^2-3n
3n(k^2 -1)
3n(k+1)(k-1)

7.(p-3)^2-49
(p-3)^2-7^2
(p-3+7)(p-3-7)
(p+4)(p-10)

8.(2x-3y)^2-(4x-y)^2
(2x-3y+4x-y)(2x-3y-(4x-y))
(6x-4y)(-2x-2y)
2(3x-2y)(-2)(x+y)
-4(3x-2y)(x+y)

9. 4a^2+16a+16
(2a)^2+2(2a)(4)+4^2
(2a+4)

10. 18c^2+12cd+2d^2
2(9c^2+6cd+d^2)
2( (3c)^2 + 2(3c)(d) + d^2)
2(3c+d)

1. 3a^2-27
=3(a^2-9)
=3(a+3)(a-3)
2. mc^2-md^2
=m(c^2-d^2)
=m(c+d)(c-d)
3. (a+b)^2-c^2
=[(a+b)+c][(a+b)-c]
=(a+b+c)(a+b-c)
4. 4x^2-(x-y)^2
=(2x)^2-(x-y)^2
=[(2x)+(x-y)][(2x)-(x-y)]
=(2x+x-y)(2x-x+y)
=(3x-y)(x+y)
5. 18b^2-8c^2
=2(9b^2-4c^2)
=2(3b+2c)(3b-2c)
6.3nk^2-3n
=3n(k^2-1)
=3n(k+1)(k-1)
7.(p-3)^2-49
=(p-3)^2-7^2
=[(p-3)+7][(p-3)-7]
=(p+4)(p-10)
8.(2x-3y)^2-(4x-y)^2
=[(2x-3y)+(4x-y)][(2x-3y)-(4x-y)]
=(6x-4y)(-2x-2y)
=-4(3x-2y)(x+y)
9. 4a^2+16a+16
=4(a^2+4a+4)
=4[(a)^2+2(a)(2)+2^2]
=4(a+2)^2
10. 18c^2+12cd+2d^2
=2(9c^2+6cd+d^2)
2(3c+d)^2

2012-10-23 16:01:19 補充：
10. 18c^2+12cd+2d^2
=2(9c^2+6cd+d^2)
=2(3c+d)^2