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)-25x 8+125x 16; (3)-a 3b 2+a 2b 3;

(4)6a 3-8a 2-4a;

(5)-x 3y 3-x 2y 2-xy; (6)a 8+a 7-2a 6-3a 5; (7)6a 3x 4-8a 2x 5+16ax 6; (8)9a 3x 2-18a 5x 2-36a 4x 4;

"3繆 (9) 27

9

3.

(10)a m -a m+1; (11)-12a 2n+1 b m+2+20a m+1 b 2nM ;

(12)x(a+b)+y(a+b);

(13)(a+b)2+(a+b); (16)a(a-b)+b(b-a);

(14)a 2b(a-b)+3ab(a-b);

(15)x( a+b-3c)-(a+b-3c)

(17)(x ・3 产(x ・3)2; (20)(x-a)3+a(a-x);

(I8)a 2b(x-y)-ab(y-x); (19)a 2(x-2a)2-a(2a-x)2;

(21)(x ・2y)(2x+3y)・2(2y ・x)(5x ・y); (24)

a(x ・y)・b(y ・x)・c(x ・y);

(22)3m(x-5)-5n(5-x);

(23)y(x ・y)2・(y ・x)3;

(25) (x・2)2・(2・xF; (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 产(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)aMb2; (4)a6-a8;

(5)x2-324; (6)144a2-256b2; (7)64x16-y4z6；(8)16a16-25b2x4;

(9)25a2b4c16-1; i- 1 A4；(10) 169 (11)36a4x1M9by；(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; (I9)(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)a<9b4; (28)a8-81b8;

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

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

(33)x2-y2 x-y;

(36)a2-4b2-2a+4b;

(38)a3-ab2-a2-ab; (39)x2+8x+16;

(37)a3-ab2+a-b;

(40)x2-12x+36;

(41)4a2・4a+1;

(42)-4a2+12ab-9b2; (43)x2・38x+36l;

(44)9x2+12xy+4y2;

(45)产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)16a2b<8ab3c2+b2c4;

(53)9(p・q)2・6(q・

(54)(a+2b)2・10(a+2b)+25; (55)4x2(a+b)2- I2xy(a+b)2+9y2(a+b)2;

p)+1;

(60)(x 2-b 2+y 2-a 2)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)=25x s (5x 8-1);

(3)=-a 2b 2(a-b);

(4)=2a(3a 2-4a-2); (5)=-xy(x 2y 2+xy+1);

(6)=a 5(a 3+a 2-2a-3);

=—xy 2 (2x 2 -3y) (7)=2ax 4(3a 2-4ax+8x 2); (8)=9a 3x 2(1-2a 2-4ax 2)=-9a 3x 2(2a 2+4ax 2-l);

(9) 27

(10)=a m (1-a)=-a m (a-1);

(11 )=4ab 2(5a m b 2n *2-3a 2n b m ); (I2)=(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); (I9)=a(x-2a)2(a-1); (20)=(x-

a)(x 2-2ax+a 2-a);

(21 )=(x-2y)(l 2x+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)(a 2+b 2+ab-a-b);

(28)=(m - a) (m -a+4x+y);

(29)=a(x-2a)2(ax-2a 2-l); (30) =(a-3)(a 3+a 2-5);

(3l)=(a-2b+3c)(5x+y); (32)=(x+2)(x-3)(x 2-x-10);

(33)=(a-b)2(a+b 2)(a+b-1); (34)=(b+c-d)(x+y-1);

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

因式分解练习二运用公式法分解因式答案

(56)(x2+y2)2・4x2y2;

Q7)宀护 °

(58)a2(x-y)+b2(y -x);

(59)4x 2-a 2-6a-9;

(1)(a+3b)(a-3b);

(2)・(3x+2y)(3x ・2y); (3) (a 2+2b)(a 2-2b);

(5)(x+18)(x ・18);

(9)(5ab 2c 8+l)(5ab 2c 8-l) (6)16(3a+4b)(3a ・4b);

(7)(8x 8+y 2z 3)(8x 8-y 2z 3);

(10)

(4)^(a +1)(a-1);

(8)(4a 8+5bx 2)(4a 8-5bx 2);