求40道数学分解因式题
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求40道数学分解因式题
额、、、作业
要包含各种解法
额、、、作业
要包含各种解法
因式分解(x+2)(x-3)+(x+2)(x+4)= .
41.因式分解2ax2-3x+2ax-3= .
42.因式分解9x2-66x+121= .
43.因式分解8-2x2= .
44.因式分解x2-x+14 = .
45.因式分解9x2-30x+25= .
46.因式分解-20x2+9x+20= .
47.因式分解12x2-29x+15= .
48.因式分解36x2+39x+9= .
49.因式分解21x2-31x-22= .
50.因式分解9x4-35x2-4= .
51.因式分解(2x+1)(x+1)+(2x+1)(x-3)= .
52.因式分解2ax2-3x+2ax-3= .
53.因式分解x(y+2)-x-y-1= .
54.因式分解(x2-3x)+(x-3)2= .
55.因式分解9x2-66x+121= .
56.因式分解8-2x2= .
57.因式分解x4-1= .
58.因式分解x2+4x-xy-2y+4= .
59.因式分解4x2-12x+5= .
60.因式分解21x2-31x-22= .
61.因式分解4x2+4xy+y2-4x-2y-3= .
62.因式分解9x5-35x3-4x= .
63.因式分解下列各式:
(1)3x2-6x= .
(2)49x2-25= .
(3)6x2-13x+5= .
(4)x2+2-3x= .
(5)12x2-23x-24= .
(6)(x+6)(x-6)-(x-6)= .
(7)3(x+2)(x-5)-(x+2)(x-3)= .
(8)9x2+42x+49= .
(1)(x+2)-2(x+2)2= .
(2)36x2+39x+9= .
(3)2x2+ax-6x-3a= .
(4)22x2-31x-21= .
70.因式分解3ax2-6ax= .
71.因式分解(x+1)x-5x= .
72.因式分解(2x+1)(x-3)-(2x+1)(x-5)=
73.因式分解xy+2x-5y-10=
74.因式分解x2y2-x2-y2-6xy+4=
x3+2x2+2x+1
a2b2-a2-b2+1
(1)3ax2-2x+3ax-2
(x2-3x)+(x-3)2+2x-6
1)(2x+3)(x-2)+(x+1)(2x+3)
9x2-66x+121
17.因式分解
(1)8x2-18 (2)x2-(a-b)x-ab
18.因式分解下列各式
(1)9x4+35x2-4 (2)x2-y2-2yz-z2
(3)a(b2-c2)-c(a2-b2)
19.因式分解(2x+1)(x+1)+(2x+1)(x-3)
20.因式分解39x2-38x+8
21.利用因式分解求(6512 )2-(3412 )2之值
22.因式分解a(b2-c2)-c(a2-b2)
24.因式分解7(x-1)2+4(x-1)(y+2)-20(y+2)2
25.因式分解xy2-2xy-3x-y2-2y-1
26.因式分解4x2-6ax+18a2
27.因式分解20a3bc-9a2b2c-20ab3c
28.因式分解2ax2-5x+2ax-5
29.因式分解4x3+4x2-25x-25
30.因式分解(1-xy)2-(y-x)2
31.因式分解
(1)mx2-m2-x+1 (2)a2-2ab+b2-1
32.因式分解下列各式
(1)5x2-45 (2)81x3-9x (3)x2-y2-5x-5y (4)x2-y2+2yz-z2
33.xy2-2xy-3x-y2-2y-1
34.因式分解y2(x-y)+z2(y-x)
1)因式分解x2+x+y2-y-2xy=
35.因式分解x2-25= .
36.因式分解x2-20x+100= .
37.因式分解x2+4x+3= .
38.因式分解4x2-12x+5= .
39.因式分解下列各式:
(1)3ax2-6ax= .
(2)x(x+2)-x= .
(3)x2-4x-ax+4a= .
(4)25x2-49= .
(5)36x2-60x+25= .
(6)4x2+12x+9= .
(7)x2-9x+18= .
(8)2x2-5x-3= .
(9)12x2-50x+8= .
(1) 答案:a(b−1)(ab+2b+a)
说明:(ab+b)2−(a+b)2 = (ab+b+a+b)(ab+b−a−b) = (ab+2b+a)(ab−a) = a(b−1)(ab+2b+a).
(2) 答案:(x−a)4
说明:(a2−x2)2−4ax(x−a)2
= [(a+x)(a−x)]2−4ax(x−a)2
= (a+x)2(a−x)2−4ax(x−a)2
= (x−a)2[(a+x)2−4ax]
= (x−a)2(a2+2ax+x2−4ax)
= (x−a)2(x−a)2 = (x−a)4.
(3) 答案:7xn−1(x−1)2
说明:原式 = 7xn−1 •x2−7xn−1 •2x+7xn−1 = 7xn−1(x2−2x+1) = 7xn−1(x−1)2.
41.因式分解2ax2-3x+2ax-3= .
42.因式分解9x2-66x+121= .
43.因式分解8-2x2= .
44.因式分解x2-x+14 = .
45.因式分解9x2-30x+25= .
46.因式分解-20x2+9x+20= .
47.因式分解12x2-29x+15= .
48.因式分解36x2+39x+9= .
49.因式分解21x2-31x-22= .
50.因式分解9x4-35x2-4= .
51.因式分解(2x+1)(x+1)+(2x+1)(x-3)= .
52.因式分解2ax2-3x+2ax-3= .
53.因式分解x(y+2)-x-y-1= .
54.因式分解(x2-3x)+(x-3)2= .
55.因式分解9x2-66x+121= .
56.因式分解8-2x2= .
57.因式分解x4-1= .
58.因式分解x2+4x-xy-2y+4= .
59.因式分解4x2-12x+5= .
60.因式分解21x2-31x-22= .
61.因式分解4x2+4xy+y2-4x-2y-3= .
62.因式分解9x5-35x3-4x= .
63.因式分解下列各式:
(1)3x2-6x= .
(2)49x2-25= .
(3)6x2-13x+5= .
(4)x2+2-3x= .
(5)12x2-23x-24= .
(6)(x+6)(x-6)-(x-6)= .
(7)3(x+2)(x-5)-(x+2)(x-3)= .
(8)9x2+42x+49= .
(1)(x+2)-2(x+2)2= .
(2)36x2+39x+9= .
(3)2x2+ax-6x-3a= .
(4)22x2-31x-21= .
70.因式分解3ax2-6ax= .
71.因式分解(x+1)x-5x= .
72.因式分解(2x+1)(x-3)-(2x+1)(x-5)=
73.因式分解xy+2x-5y-10=
74.因式分解x2y2-x2-y2-6xy+4=
x3+2x2+2x+1
a2b2-a2-b2+1
(1)3ax2-2x+3ax-2
(x2-3x)+(x-3)2+2x-6
1)(2x+3)(x-2)+(x+1)(2x+3)
9x2-66x+121
17.因式分解
(1)8x2-18 (2)x2-(a-b)x-ab
18.因式分解下列各式
(1)9x4+35x2-4 (2)x2-y2-2yz-z2
(3)a(b2-c2)-c(a2-b2)
19.因式分解(2x+1)(x+1)+(2x+1)(x-3)
20.因式分解39x2-38x+8
21.利用因式分解求(6512 )2-(3412 )2之值
22.因式分解a(b2-c2)-c(a2-b2)
24.因式分解7(x-1)2+4(x-1)(y+2)-20(y+2)2
25.因式分解xy2-2xy-3x-y2-2y-1
26.因式分解4x2-6ax+18a2
27.因式分解20a3bc-9a2b2c-20ab3c
28.因式分解2ax2-5x+2ax-5
29.因式分解4x3+4x2-25x-25
30.因式分解(1-xy)2-(y-x)2
31.因式分解
(1)mx2-m2-x+1 (2)a2-2ab+b2-1
32.因式分解下列各式
(1)5x2-45 (2)81x3-9x (3)x2-y2-5x-5y (4)x2-y2+2yz-z2
33.xy2-2xy-3x-y2-2y-1
34.因式分解y2(x-y)+z2(y-x)
1)因式分解x2+x+y2-y-2xy=
35.因式分解x2-25= .
36.因式分解x2-20x+100= .
37.因式分解x2+4x+3= .
38.因式分解4x2-12x+5= .
39.因式分解下列各式:
(1)3ax2-6ax= .
(2)x(x+2)-x= .
(3)x2-4x-ax+4a= .
(4)25x2-49= .
(5)36x2-60x+25= .
(6)4x2+12x+9= .
(7)x2-9x+18= .
(8)2x2-5x-3= .
(9)12x2-50x+8= .
(1) 答案:a(b−1)(ab+2b+a)
说明:(ab+b)2−(a+b)2 = (ab+b+a+b)(ab+b−a−b) = (ab+2b+a)(ab−a) = a(b−1)(ab+2b+a).
(2) 答案:(x−a)4
说明:(a2−x2)2−4ax(x−a)2
= [(a+x)(a−x)]2−4ax(x−a)2
= (a+x)2(a−x)2−4ax(x−a)2
= (x−a)2[(a+x)2−4ax]
= (x−a)2(a2+2ax+x2−4ax)
= (x−a)2(x−a)2 = (x−a)4.
(3) 答案:7xn−1(x−1)2
说明:原式 = 7xn−1 •x2−7xn−1 •2x+7xn−1 = 7xn−1(x2−2x+1) = 7xn−1(x−1)2.