初二数学因式分解 分式方程专项归纳 下载本文

22??1??1???122?(5)??x?y???x?y???x?2y?

??2?????2??2?(6)先化简,再求值:?x?2y??2x?4y???9x3y?12xy3?3xy2????3xy?,其中x?1,y?2

33、乘法公式运算: (1)(3x+2)(3x-2);

(2)(b+2a)(2a-b) (4) (x+2)(x-3)

(6)(x+3)2-(x+2)(x-2).

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(3)(-x+2y)(-x-2y)

(5)(y+2)(y-2)-(y-1)(y+5)

(7)(a+b)(a-2b)-(a+2b)(a-b) (8)5x(x+2x+1)-(2x+3)(x-5).

(9)4292-1712.

(10)已知

2?a?b?2?11,?a?b??5,求(1)a2?b2;(2)ab

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2

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(11)若(x+px+q)(x-2x-3)展开后不含x,x项,求p、q的值

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(12)已知 (a-b)2=7, (a+b)2=13, 试求a2+b2和ab的值; (13)已知:x2+y2+4x-6y+13=0,x、y均为有理数,求xy的值.

(14)已知5x2-2xy+y2+4x+1=0,求x、y的值.

(15)当a,b为何值时,多项式a+b-4a+6b+18有最小值?并求出这个最小值.

2

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(16)已知a=1990x+1989,b=1990x+1990,c=1990x+1991,求a2+b2

+c2-ab-ac-bc的值

(17)若a,b,c是三角形的三边,且满足关系式a2+b2+ c2-ab-ac-bc

=0,试判断这个三角形的形状

(18)已知2x?y?10,求?(x2?y2)?(x?y)2?2y(x?y)??4y的值

(19)已知x2+y2=25,x+y=7,且x>y,求x-y的值

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(20)已知:m2?n?2,n2?m?2(m?n) 求:m3?2mn?n3的值 (21)已知9x2?12xy?8y2?4yz?2z2?4z?4?0,求x、y、z的值

a2a(22)已知2的值 ?6,试求4a?a2?1a?a?1(23)x2?112?(x?)? 2xx =(x?1)2+

x1x2(24)已知x?1?3,则x2?x= 1? 2x1(x?)2= x .

(26)已知:x2+3x+1=0.x2? (27)已知x?y?8,x2?y2?16,则x?y?____

(28)如果(2a+2b+1)(2a+2b-1)=63,那么a+b的值为 (29)已知x+y=1,那么1x2+xy+1y2的值为

22(30)已知m+m-1=0,则m+2m+2004=

2

3

2

(31)已知:a+b=8,ab=16+c2,求(a-b+c)2002的值. 2、分解因式: (1)x3-4x

(2)8a4-2a2

(3)m2-n2-3m-3n (4)x2+2xy+y2-4

(5)2x2+5xy-x (6)2x2y+5xy2-xy (7)-4x4-6x3+2x2

(8)-4x4y-6x2y3+2xy4

(9)2a(x-2y)-3b(x-2y)

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(10)2a(x-2y)-3b(2y-x)-4c(x-2y)

(11)4(a-2b)2-9(2a+b)2 (12)9(a+b)2+6(a+b)+1

(13)?1211x?xy?y2 439

(14)3p?x?1?y?6p?x?1?y?3p?x?1?

222(15)m2(p-q)-p+q

(16)a(ab+bc+ac)-abc;

(18)abc(a2+b2+c2)-a3bc+2ab2c2;

(17)x4-2y4-2x3y+xy3

(19)a2(b-c)+b2(c-a)+c2(a-b) (20)(x2-2x)2+2x(x-2)+1 (21)(x-y)2+12(y-x)z+36z2

(22)x2-4ax+8ab-4b2;

(23)(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx) (24)(1-a2)(1-b2)-(a2-1)2(b2-1)2; (25)(x+1)2-9(x-1)2

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(26)4a2b2-(a2+b2-c2)2; (28)x3n+y3n;

(30)(3m-2n)3+(3m+2n)3; (32)8(x+y)3+1; (34)x2+4xy+3y2; (36)x4+2x2-8; (38)x5-2x3-8x;

(27)ab2-ac2+4ac-4a (29)(x+y)3+125

(31)x6(x2-y2)+y6(y2-x2) (33)(a+b+c)3-a3-b3-c3 (35)x2+18x-144

(37)-m4+18m2-17

(39)x8+19x5-216x2

(41)5+7(a+1)-6(a+1)2 (43)x2+y2-x2y2-4xy-1 (45)x2-y2-x-y (47)m4+m2+1

(48)a3-ab2+a-b

(50)x6-y6+3x2y4-3x4y2

(52)m2-a2+4ab-4b2

(40)(x2-7x)2+10(x2-7x)-24;

(42)(x2+x)(x2+x-1)-2;

(44)(x-1)(x-2)(x-3)(x-4)-48; (46)ax2-bx2-bx+ax-3a+3b; (47)a2-b2+2ac+c2;

(49)625b4-(a-b)4;

(51)x2+4xy+4y2-2x-4y-35;

(53)5m-5n-m2+2mn-n2.

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