因式分解的基礎知識.doc

1、1、用提公因式法：(I) 4ai3b2-6ab3c=; (2) 3x2-6xy+x=;(3) -4m3+i6m2-6m=; (4) ax+ay=; (5) 4a2+10ab=;(6) -x2+xy-xz=; (7) -24x2y-12xy 2+28y3=;(8) 56x3yz+14x2y2z-21xy2z2=; a ( x+y) +b (x+y ) =(9) 2a ( b+c) -3 ( b+c) =; (10) 5x (x-y) +2y (x-y ) =(II) (m+n) (p+q) - ( m+n) (p-q) =; (12) a( a-b) + (a-b) 2=(13) (2a+b)

2、(2a-3b) -3a ( 2a+b) =;2、把下列多項式分解因式：(1) p (x-y) -q ( y-x)(2) m ( a-3) +2 (3-a)(3) (a+b) (a-b) - ( b+a)(4) a (x-a ) +b (a-x ) -c (x-a)(5 ) 10a (x-y) 2-5b (y-x )(6 ) 3 (x-1) 3y- (1-x ) 2z3、用公式因式分解：1(1) a2- x2=; 36-m2=; 4x2-9y2=9(2 ) 36n2-仁； 25p2-49q2=; 0.81a2-16b2=;(3 ) 121x2-4y2=； a2 p2-b2q2=; x2-2x+1

3、=;(4) a2+8a+16=; 1-4t+4t 2=; m2 14m+49=；1(5) b2 22b+12仁; y2+y+ =； 25a2+80a+64=;4(6) a2b2 4ab+4=; 16 8xy+x 2y2=； 2xy-x2-y2=；4、把下列多項式因式分解：(1)4a2-(b+c)2；(2)( 3m+2n) 2(m n)2;(3)2ab3-2ab;(4) 1-a4;(5) x3-16x;(6) x4+16(7) (2x+y) 2(x+2y) 2;(8) (a+b+c) 2( a+b c) 2(9) 81a4 b4;(10) 8y4 2y2;(11) 3ax2 3ay2;5、把下列

4、多項式分解因式：(1) (X+Y ) +6 (X+Y ) +92 2(2) (m+n)+4m (m+n) +4m ；(3) 3-6x+3x2;(4) -a+2a2-a3;(5) a4-2a2b2+b4；(6) (x2+9) 236x2；(7) 4-12 (x-y ) +9 (x-y ) 2;(8) 4x2 (a+b) 2-12xy (a+b) +9y2；(9) 20a3x3-45axy2；(10) a3-4a2b+4ab2；(11) a4-8ab+16b4；1(12) a4x2+4a2x2y+4x2y2；(13) 16a2b4-8ab3c2+b2c4；(14) a4-2a2+116(15) a2 (a-b) +b2 (b-a)；(16) (y2-6) 2-6 (y2-6) +9 ；(17) -x4+2x2y2-y4；(18) (x-a ) (21) 4(x+y+z) -9(x-y-z)+a(a-x)(20) a5