提公因式、公式法因式分解專題

1、.因式分解練習(xí)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)am-am+1;(11)-12a2n+1bm+2+20am+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)(

2、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

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)(x3);(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);因式分解練習(xí)二運(yùn)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

4、-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

5、+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

6、-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-

7、a2)2-4(ab-xy)2;因式分級(jí)答案因式分解練習(xí)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)=am(1-a)=-am(a-1);(11)=4ab2(5amb2n+2-3a2nbm);(12)=(x+y)(a+b);(13)=(a+b)(a+b+1);(14)=ab(a-b)(a+3);

8、(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

9、);(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);因式分解練習(xí)二運(yùn)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)(5ab

10、2c8+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

11、); (22)-(a+c)(a-2b+c);(23)(3a+b)(b-a); (24)-(3x-4y+5z)(x-2y+3z)0(25)-(5x-y-z)(x-5y-5z); (26)a(1+a2)(1+a)(1-a);(27)(a2+3b2)(a2-3b2); (28)(a4+9b4)(a2+3b2)(a2-3b2);(29)a(a4+b)(a4-b); (30)(a8+b8)(a4+b4)(a2+b2)(a+b)(a-b);(31)a2b(b+2)(b-2); (32)(x-y)(x+y+1); (33)(x+y)(x-y-1);(34)(x-y)(x+y-1); (35)(a+2b)(a-2b-1);(36)(a-2b)(a+2b-2) (37)(a-b)(a2+ab+1)(38)a(a+b)(a-b-1) (39)(x+4)2;(40)(x-6)2; (41)(2a-1)2;(42)-(2a-3b)2; (43)(x-19)2;(44)(3x+2y)2; (45)(y-25x)2;(46)-4(a-1)2; (47)(x3+12)2;(48)(3ab3-1)2; (49)(7a-8b)2;(50)a(a-2b)2; (51)x2(a2+2y)2;(52)b2(4ab-