經(jīng)典因式分解練習(xí)題附答案

1、因式分解練習(xí)題一、填空題：1. 4r+ 85+ 24好 4a()；2. (a 3)(3 2a尸(3 a)(3 2a);3. a3b- ab=ab(a-b)()；4. (1 - a)mn+ a 1 = ( )(mn- 1)?5. 0,0009h4 = ( )3;6. 1-()+J = G )37. ( )a3 - 6a+1 = ( )2;g. 8x3 _ ( ) = (2x-)(+6x+9)；9. x2 - y2 - z2 + 2yz = x2 - ( ) = ( X10. 2ax- 10ay+ 5by _bx= 2a( ) -b()=()()；IL x2 + 3x_ 10 = (x )(x)；

2、12. 若 m2 3m + 2=(m + a)(m + b),則 a=? b=;s1 3113. x - -y =(x- -y)()； Q614. a? be + ab- ac =(J + &b)()=()();15. 當(dāng)m=時(shí)，x2+2(m3)x + 25是完全平方式.三、因式分解：21. m (p q) p+q;2. a(ab+ bc+ac)abc;f.o-.q-B-.(o + q + e) 金 匕匕匕匕f 1，+ (A + x)8匕Cx- A) A + ( A- x) x 力OO wO O w(us+uj£)+ (us-uj£)匕匕，9"+aS+x)

3、 4L匕fu A+U X -Pi匕匕tep-oep + pe-cie el尹+尹）一君歸7，一x)64 + x)GG，式尹）一Qq DQbD .（hf (xq - Ae)(Aq +xb)乙 + (xq -Ae) + (Aq+xe) GG.6f qtz-qeg +xet7- x gGG/9£ + z(x 位工+加一x)f|, + (S-x)xs + 2(xs-2x) -9(q B)廣 + (B o)R + (o-q)2e，尹丹巳4+oq©B (4+汨+尹)oqe >feAx + Aexs-/s-/ £21. x2 + 18x144;22. x4+2x2 8;2

4、3. -m4+18m2-17;24. x5 2x38x;25. x8 + 19x5 216x2;26. (x2 7x)2+ 10(x2 7x) 24;27. 5+7(a+ 1)-6(a+ 1)2;28. (x2+ x)(x2 + x 1)2;29. x2 + y2 x2y2 4xy1;30. (x - 1)(x - 2)(x - 3)(x - 4) - 48;四、證明(求值)：1,已知 a+ b=0,求 a3 2b3 + a2b2at2 G值.2 .求證：四個(gè)連續(xù)自然數(shù)G積再加上1, 一定是一個(gè)完全平方數(shù).3 .證明：(ac bd)2+ (bc+ad)2=(a2+ b2)(c2+ d2).4.

5、已知 a=k+ 3, b=2k+2, c=3k1,求 a2+b2+c2 + 2ab 2bc 2acG值.5 .若 x2+mx+n=(x 3)(x + 4),求(m+n)2G值.6 .當(dāng)a為何值時(shí)，多項(xiàng)式x2 + 7xy+ay2 5x + 43y 24可以分解為兩個(gè)一次因式G乘積.7 .若x, y為任意有理數(shù)，比較6xy與x2+9y2G大小.8 .兩個(gè)連續(xù)偶數(shù)G平方差是4 G倍數(shù).參考答案:、填空題:L a2 + 2a + 6 4- 1-a,2. 5, 0.03x2 7. 9, (3a1)" ?''%119, g_工) x _ y +“ x + y-3- a+b 6.

6、-x,-2410. x 5y, x 5y, x 5y, 2a b11. +5, 212. 1, 2(或一2, 1)13. x2+ -xy+ -y22414. bc+ac, a+ b, ac15. 8 或一2三、因式分解：1. (pq)(m1)(m+1).2. a2(b+c),3.原式=x(Y + /) - 2y(x3 + yJ) = (x3 +y3)(x_ 2y) = (x-2y)(x+y) (x3-xy + y3).4, abc(b+。)、5,原式=a2b - aJc + bic - ab + (a - b) = (a°b - ab)- (a2c -b2c) + / (a - b)

7、 = ab(a -b) - c(a2 -b2) + c2 (a - b) = (a - b)ab - c(a+ b) + c3 =(a - b)a(b - c) - cfb - c) = (a - b)(b - c)(a - c).6.原式=電-2),+ 2x(x-2) +la =x(x-2)+ I2 = (xa -2x+ l)a7. (x-y-6»8. (x 2b)(x4a+ 2b).9. (ax + by+ ay -bx)a.10. (1 - a)(l + 20(1 -b)(l+b)(a3 + ba - aab3),11. 4(2x-1)(2-x).12. JE = (2ab +

8、 aa+ba-ca)(2ab-aa-ba + ca)=Ka+b)a -ca c2 - (a- b)2 = (a + b+ c)(a+ b - c)c + ab)(c - a + b5.13. 原式=a(b2 -c2 + 4c - 4) = a(b2 - c2 + 2b - 2b+ 2c+ 2c 7) =a(b - c)(b + c) + 2(b+ c) - 2(b - c) - 4 = a(b - c) + 2(b + c) - 2 =- c + 2)(b + c - 2).14. (F +)(戶婢).15. (x + y+ 5)(zJ + 2xy+ y2 - 5x - 5y+ 25)416.

9、 18m(3m2 + 4n2).17,原式=(-一產(chǎn)(d-刑=3 +力僅-y)幻+ )(- -y) = (x + y)2(x y)，1-對(duì)+ /)(/ + xy+ ya).(2x+2y+l)(4x口 + 8即+ 4/ - 2x - 2y + 1).19. 3(b+ c)(a + b)(c + a).提示上 原式二(a+b+c)，-/-。二+(?).20. (x + 3y)(x + y).21. (x-6)(x + 24).22. 興-2)(/+ 4).23. - (m2 - 17)(m+ l)(m - 1).24. + 2)(x - 2)(，+ 2) .25.原式= S(x" + 1

10、9F -210=/(f+ 27)(婷-8) =xx+ 3)-3x + 9)(x - 2)(/ + 2x+ 4).26. (x-3)(x-4)(xa-7x-2).27. (3 + 2a)(2-3a).28 .原式=(，+ 初* + x) -l-2 = (x3 + x)a - (；xa + x) - 2 = (x2 + x - 2)(1 + 漢+ 1) = (x+ 2)(x 7)(/ +x+ 1).29 .原式=(Y - 2xy + ya)(xaya + 2xy + 1) = (x -y)3 - (xy+ l)a = (x - y + xy + )(x - y - xy -1).30,原式=,7)

11、(漢-4)(x -2)(籃一3)-48=(1 -回+4(-融) + 6-48 =那為n + 10(1 - 劉-24 = (/ 5K +12)甘一%-2).四、證明(求值)：1,原式二(a3+aJb)(2b3 + 2ab3) =aa(a+b) -2ba(a+b)=0.2 .提示：設(shè)四個(gè)連續(xù)自然數(shù)為 n, n+1, n+2, n + 3n(n + 1)( 口 + 2)(口 + 3) + 1 =(/ + 3n)(n2 + 3n+ 2) + l = (n2 + 3n)2 + 2(1? + 3n) + 1 = (n2 + 3n + I)2 .3 .證明士(就-bdy + (bc+皆d)，=員- 2貧bcd + b4 + bY + 2abcd+ a2d2 = a2(c2 + d2).4 .提不：aJ + b2 + c2 + 2ab 2bc - 2ac =(a + b)2 - 2c(a+ b) + c2 =(a + b - c)3 = (k+ 3+ 2k+ 2 + 3k+ 1)，= 36.5,提不：m = 1, n = T2； (m+療= 121.6.提示：a=-18.令/ + 7xy+ay2 -5x+43y - 24 = (x + my+ n)(x + py+q) =，+(in + p)xy + mpy2 + (q + n)x+ (mq +