提公因式、公式法因式分解专题

因式分解练习一

提取公因式法分解因式

(1)-15ax-20a; (2)-25x8+125x16; (3)-a3b2+a2b3; (4)6a3-8a2-4a; (5)-x3y3-x2y2-xy; (6)a8+a7-2a6-3a5; (7)6a3x4-8a2x5+16ax6; (8)9a3x2-18a5x2-36a4x4; (9)(10)a m-a m+1; (11)-12a2n+1b m+2+20a m+1b2n+4; (12)x(a+b)+y(a+b);

(13)(a+b)2+(a+b); (14)a2b(a-b)+3ab(a-b); (15)x(a+b-3c)-(a+b-3c) (16)a(a-b)+b(b-a);

(17)(x-3)3-(x-3)2; (18)a2b(x-y)-ab(y-x); ( 19)a2(x-2a)2-a(2a-x)2; (20)(x-a)3+a(a-x);

(21)(x-2y)(2x+3y)-2(2y-x)(5x-y); (22)3m(x-5)-5n(5-x); (23)y(x-y)2-(y-x)3; (24)a(x-y)-b(y-x)-c(x-y);

(25)(x-2)2-(2-x)3; (26)m(n-2)-p(2-n)+(n-2); (27)a3-b3-a2+b2; (28)(m-a)2+3x(m-a)-(x+y)(a-m);

(29)a2(x-2a)3-a(2a-x)2; (30)(a-3)(a3-2)-(3-a)(a2-1)+2(3-a); (31)2(x-y)(a-2b+3c)-3(x+y)(2b-a-3c);

(32)(x+2)(x-3)(x2-7)+(2+x)(3-x)(x＋3); (33)(a-b)2(a+b)3-(b-a)2(b+a)2; (34)x(b+c-d)-y(d-b-c)-b-c+d;

(35)(x+1)2(2x-3)+(x+1)(2x-3)2-(x+1)(3-2x);

因式分解练习二

运用公式法分解因式；

(1)a2-9b2; (2)-9x2+4y2; (3)a4-4b2; (4)a6-a8;

(5)x2-324; (6)144a2-256b2; (7)64x16-y4z6; (8)16a16-25b2x4; (9)25a2b4c16-1; (10)(11)36a4x10-49b6y8; (12)81x8-225a4b4; (13)(a+b)2-100; (14)-z2+(x-y)2; (15)361-(3a+2b)2; (16)(ax+by)2-1; (17)20a3x3-45axy2; (18)(2x-3y)2-4a2; (19)(a+2b)2-(x-3y)2; (20)4(a+2b)2-25(a-b)2; (21)a2(a+2b)2-9(x+y)2; (22)b2-(a-b+c)2; (23)(a+b)2-4a2; (24)(x-y+z)2-(2x-3y+4z)2;

(25)4(x+y+z)2-9(x-y-z)2; (26)a-a5; (27)a4-9b4; (28)a8-81b8;

(29)a9-ab2; (30)a16-b16; (31)a2b3-4a2b; (32)x2-y2+x-y;

(33)x2-y2-x-y; (34)x2-y2-x+y; (35)a2-4b2-a-2b; (36)a2-4b2-2a+4b;

(37)a3-ab2+a-b; (38)a3-ab2-a2-ab; (39)x2+8x+16; (40)x2-12x+36;

(41)4a2-4a+1; (42)-4a2+12ab-9b2; (43)x2-38x+361; (44)9x2+12xy+4y2;

(45)y2-50xy+625x2; (46)8a-4a2-4; (47)x6+24x3+144; (48)1-6ab3+9a2b6; (49)49a2-112ab+64b2; (50)a3-4a2b+4ab2; (51)a4x2+4a2x2y+4x2y2; (52)16a2b4-8ab3c2+b2c4; (53)9(p-q)2-6(q-p)+1; (54)(a+2b)2-10(a+2b)+25; (55)4x2(a+b)2-12xy(a+b)2+9y2(a+b)2;

(56)(x2+y2)2-4x2y2; (57)(58)a2(x-y)+b2(y-x); (59)4x2-a2-6a-9;

(60)(x2-b2+y2-a2)2-4(ab-xy)2;

因式分级答案

因式分解练习一答案：

三、(1)=-5a(3x+4); (2)=25x8(5x8-1); (3)=-a2b2(a-b); (4)=2a(3a2-4a-2); (5)=-xy(x2y2+xy+1); (6)=a5(a3+a2-2a-3);

(7)=2ax4(3a2-4ax+8x2); (8)=9a3x2(1-2a2-4ax2)=-9a3x2(2a2+4ax2-1); (9)(10)=a m(1-a)=-a m(a-1);

(11)=4ab2(5a m b2n+2-3a2n b m); (12)=(x+y)(a+b); (13)=(a+b)(a+b+1); (14)=ab(a-b)(a+3); (15)=(a+b-3c)(x-1);

(16)=(a-b)2; (17)=(x-3)2(x-4); (18)=ab(x-y)(a+1); (19)=a(x-2a)2(a-1); (20)=(x-a)(x2-2ax+a2-a);

(21)=(x-2y)(12x+y); (22)=(x-5)(3m+5n); (23)=x(x-y)2; (24)=(x-y)(a+b-c); (25)=(x-2)2(x-1);

(26)=(n-2)(m+p+1); (27)=(a-b)(a2+b2+ab-a-b); (28)=(m-a)(m-a+4x+y); (29)=a(x-2a)2(ax-2a2-1);

(30)=(a-3)(a3+a2-5); (31)=(a-2b+3c)(5x+y); (32)=(x+2)(x-3)(x2-x-10); (33)=(a-b)2(a+b2)(a+b-1);

(34)=(b+c-d)(x+y-1); (35)=(x+1)(2x-3)(3x-1);

因式分解练习二运用公式法分解因式答案

(1)(a+3b)(a-3b); (2)-(3x+2y)(3x-2y); (3)(a2+2b)(a2-2b); (4)-a6(a+1)(a-1);

(5)(x+18)(x-18); (6)16(3a+4b)(3a-4b); (7)(8x8+y2z3)(8x8-y2z3); (8)(4a8+5bx2)(4a8-5bx2); (9)(5ab2c8+1)(5ab2c8-1) (10);

(11)(6a2x5+7b3y4)(6a2x5-7b3y4); (12)9(3x4+5a2b2)(3x4-5a2b2);

(13)(a+b+10)(a+b-10); (14)(x-y+z)(x-y-z);

(15)(19+3a+2b)(19-3a-2b); (16)(ax+by+1)(ax+by-1);

(17)5ax(2ax+3y)(2ax-3y); (18)(2x-3y+2a)(2x-3y-2a);

(19)(a+2b+x-3y)(a+2b-x+3y); (20)-3(7a-b)(a-3b);

(21)(a2+2ab+3x+3y)(a2+2ab-3x-3y); (22)-(a+c)(a-2b+c);

(23)(3a+b)(b-a); (24)-(3x-4y+5z)(x-2y+3z)0