F.3 Maths 因式分解

1. (2+k)"-9
=k"+4k+4-9
=k"+4k-5
=(k+5)(k-1)

2.169-(m-7n)"
=13"-(m-7n)"
=[13-(m-7n)][13+(m-7n)]

3. (a-1)"-(b-1)"
=[(a-1)+(b-1)][(a-1)-(b-1)]
=(a+b+2)(a-b)
=(a"+ab+2a)-(ab+b"+2b)
=a"-b"+2a-2b
=(a+b)(a-b)+2(a-b)
=(a-b)[(a+b)+2]

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

5.28(x=y)"-7(x-y)"
=7[4(x+y)"-(x-y)"]
=7[2(x+y)+(x-y)][2(x+y)-(x-y)]
=7[3x+y][x+3y]

6.a"-b"+bc-ac
=(a+b)(a-b)-(a-b)c
=(a-b)(a+b-c)

7.4c"-9d"-2c-3d
=(2c+3d)(2c-3d)-(2c+3d)
=(2c+3d)(2c-3d-1)

8.12v-12v"-6u+3u"
=3(4v-4v"-2u+u")
=3[(2v+u)(2v-u)+2(2v-u)]
=3(2v-u)(2v+u+2)

1.k''+4k-5
2.169-m''+14mn-49n''
3.a"-b''-2a+2b
4.9x''+y"-z"+9xy+4z-4
5.70xy


6.(a-b)(a-b-c)
7.2c(2c-1)-3d(3d-1)
8.3(4v-4v"+u"-2u)