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因式分解练习题及答案,初一因式分解练习题及答案

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因式分解练习题及答案,求!!!

140.m2(p-q)-p+q

因式分解练习题及答案,初一因式分解练习题及答案

141.(2m+3n)(2m-n)-4n(2m-n).

142.(x+2y)2-x2-2xy.

143.a(ab+bc+ac)-abc.

144.ab-a-b+1.

145.xyz-xy-xz+x-yz+y+z-1.

146.x4-2y4-2x3y+xy3.

148.abc(a2+b2+c2)-a3bc+2ab2c2.

149.(a-b-c)(a+b-c)-(b-c-a)(b+c-a).

150.a2(b-c)+b2(c-a)+c2(a-b).

a(a+b)(a-b)-a(a+b)2.

152.(x2-2x)2+2x(x-2)+1.

153.2acd-c2a-ad2.

154.(x-y)2+12(y-x)z+36z2.

156.x2-4ax+8ab-4b2.

157.a2b2+c2d2-2abcd+2ab-2cd+1.

158.(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx).

160.(1-a2)(1-b2)-(a2-1)2(b2-1)2.

161.3x4-48y4.

162.(x+1)2-9(x-1)2.

163.(x2+pq)2-(p+q)2x2.

164.(1+2xy)2-(x2+y2)2.

165.4a2b2-(a2+b2)2.

166.4a2b2-(a2+b2-c2)2.

167.(c2-a2-b2)2-4a2b2.

168.(x2-b2+y2-a2)2-4(ab-xy)2.

169.64a4(x+1)2-49b4(x+1)4.

170.ab2-ac2+4ac-4a.

171.4a2-c2+6ab+3bc.

172.x3n+y3n.

174.(x+y)3+125.

176.(m-n)6-(m+n)6.

177.(x+1)6-(x-1)6.

178.a12-b12.

179.(z-x)3-(y+z)3.

180.(3m-2n)3+(3m+2n)3.

181.x6(x2-y2)+y6(y2-x2).

182.8(x+y)3+1.

183.(a-1)3-(b+1)3.

184.(a+b+c)3-a3-b3-c3.

185.x2+4xy+3y2.

186.x2y2-18xy+65.

187.x2+18x-144.

188.x2+30x+144.

189.x4+2x2-8.

190.3x4+6x2-9.

191.-m4+18m2-17.

192.3x4-7x2y2-20y4.

193.x5-2x3-8x.

194.a3-5a2b-300ab2.

195.x8+19x5-216x2.

196.6a4n+k-a2n+k-35ak.

199.30x2+8xy-182y2.

200.m4+14m2-15.

140.(p-q)(m-1)(m+1).

141.(2m-n)2.

142.2y(x+2y).

143.a2(b+c).

144.(b-1)(a-1).

145.(x-1)(y-1)(z-1).

提示:方法一原式=x(yz-y-z+1)-(yz-y-z+1)

=(yz-y-z+1)(x-1)

=[y(z-1)-(z-1)](x-1)

=(x-1)(y-1)(z-1).

方法二原式=xy(z-1)-x(z-1)-y(z-1)+(z-1)

=(xy-x-y+1)(z-1)

=[x(y-1)-(y-1)](z-1)

=(x-1)(y-1)(z-1).

146.(x-2y)(x+y)(x2-xy+y2).

提示:方法一原式=x(x3+y3)-2y(x3+y3)

=(x3+y3)(x-2y)

=(x-2y)(x+y)(x2-xy+y2).

方法二原式=x3(x-2y)+y3(x-2y)

=(x-2y)(x3+y3)

=(x-2y)(x+y)(x2-xy+y2).

148.abc(b+c)2.

提示:原式=abc(a2+b2+c2-a2+2bc).

149.2(b-c)(a-b-c).

提示:原式=(a-b-c)(a+b-c)+(a-b-c)(b-c-a)

=(a-b-c)[(a+b-c)+(b-c-a)]

=2(b-c)(a-b-c).

150.(a-b)(b-c)(a-c).

提示:原式=a2b-a2c+b2c-ab2+c2(a-b)

=(a2b-ab2)-(a2c-b2c)+c2(a-b)

=ab(a-b)-c(a2-b2)+c2(a-b)

=(a-b)[ab-c(a+b)+c2]

=(a-b)[a(b-c)-c(b-c)]

=(a-b)(b-c)(a-c).

提示:原式=a(a+b)[a-b-(a+b)]=a(a+b)(-2b)

=-2ab(a+b);

152.(x-1)4.

提示:原式=[x(x-2)]2+2•x(x-2)+12

=[x(x-2)+1]2=(x2-2x+1)2

=(x-1)4.

153.-a(c-d)2.

154.(x-y-6z)2.

156.(x-2b)(x-4a+2b).

157.(ab-cd+1)2.

提示:原式=(a2b2-2abcd+c2d2)+2(ab-cd)+1

=(ab-cd)2+2(ab-cd)+1

=(ab-cd+1)2.

158.(ax+by+ay-bx)2.

160.(1+a)(1-a)(1+b)(1-b)(a2+b2-a2b2).

161.3(x2+4y2)(x+2y)(x-2y).

162.4(2x-1)(2-x).

163.(x2+px+qx+pq)(x2-px-qx+pq).

164.(1+x-y)(1-x+y)(x2+y2+2xy+1).

165.-(a+b)2(a-b)2.

166.(a+b+c)(a+b-c)(c+a-b)(c-a+b).

提示:原式=(2ab+a2+b2-c2)(2ab-a2-b2+c2)

=[(a+b)2-c2][c2-(a-b)2]

=(a+b+c)(a+b-c)(c+a-b)(c-a+b).

167.(c+a-b)(c-a+b)(c+a+b)(c-a-b).

168.(x+y+a+b)(x+y-a-b)(x-y+a-b)(x-y-a+b).

提示:原式=(x2-b2+y2-a2+2ab-2xy)(x2-b2+y2-a2-2ab+2xy)

=[(x2-2xy+y2)-(a2-2ab+b2)][(x2+2xy+y2)

-(a2+2ab+b2)]

=[(x-y)2-(a-b)2][(x+y)2-(a+b)2]

=(x-y+a-b)(x-y-a+b)(x+y+a+b)(x+y-a-b).

169.(x+1)2(8a2+7b2x+7b2)(8a2-7b2x-7b2).

170.a(b-c+2)(b+c-2).

提示:原式=a(b2-c2+4c-4)

=a(b2-c2+2b-2b+2c+2c-4)

=a[(b-c)(b+c)-2(b-c)+2(b+c)-4]

=a[(b-c)+2][(b+c)-2].

171.(2a+c)(2a-c+3b).

172.(xn+yn)(x2n-xnyn+y2n).

174.(x+y+5)(x2+2xy+y2-5x-5y+25).

176.-4mn(3n2+m2)(3m2+n2).

提示:原式=[(m-n)3]2-[(m+n)3]2

=[(m-n)3+(m+n)3][(m-n)3-(m+n)3]

=2m[(m-n)2-(m-n)(m+n)(m+n)2]

×{-2n[(m-n)2+(m-n)(m+n)+(m+n)2]}

=-4mn(m2+3n2)(3m2+n2).

177.4x(x2+3)(3x2+1).

提示:原式=[(x+1)3]2-[(x-1)3]2

=[(x+1)3+(x-1)3][(x+1)3-(x-1)3]

=2x[(x+1)2-(x+1)(x-1)+(x-1)2]

×2[(x+1)2+(x+1)(x-1)+(x-1)2]

=4x(x2+3)(3x2+1).

178.(a-b)(a+b)(a2+b2)(a2+ab+b2)(a2-ab+b2)(a4-a2b2+b4).

提示:原式=(a6)2-(b6)2=(a6+b6)(a6-b6)

=[(a2)3+(b2)3][(a3)2-(b3)2]

=(a2+b2)(a4-a2b2+b4)(a3+b3)(a3-b3).

179.-(x+y)(x2+y2+3z2-xy+3yz-3xz).

180.18m(3m2+4n2).

181.(x+y)2(x-y)2(x2-xy+y2)(x2+xy+y2).

提示:原式=(x2-y2)(x6-y6)

=(x+y)(x-y)(x3+y3)(x3-y3).

182.(2x+2y+1)(4x2+8xy+4y2-2x-2y+1).

183.(a-b-2)(a2+ab+b2-a+b+1).

184.3(b+c)(a+b)(c+a).

提示:原式=[(a+b+c)3-a3]-(b3+c3).

185.(x+3y)(x+y).

186.(xy-13)(xy-5).

187.(x-6)(x+24).

188.(x+6)(x+24).

189.(x2-2)(x2+4).

190.3(x2+3)(x+1)(x-1).

191.(m2-17)(1+m)(1-m).

192.(3x2+5y2)(x+2y)(x-2y).

193.x(x+2)(x-2)(x2+2).

194.a(a-20b)(a+15b).

195.x2(x+3)(x2-3x+9)(x-2)(x2+2x+4).

提示:原式=x2(x6+19x3-216)

=x2(x3+27)(x3-8)

=x3(x+3)(x2-3x+9)(x-2)(x2+2x+4).

196.ak(2a2n-5)(3a2n+7).

199.2(3x-7y)(5x+13y).

200.(m2+15)(m+1)(m-1).

201.m2(p-q)-p+q;

202.a(ab+bc+ac)-abc;

203.x4-2y4-2x3y+xy3;

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

205.a2(b-c)+b2(c-a)+c2(a-b);

206.(x2-2x)2+2x(x-2)+1;

207.(x-y)2+12(y-x)z+36z2;

208.x2-4ax+8ab-4b2;

209.(ax+by)2+(ay-bx)2+2(ax+by)(ay-bx);

210.(1-a2)(1-b2)-(a2-1)2(b2-1)2;

211.(x+1)2-9(x-1)2;

212.4a2b2-(a2+b2-c2)2;

213.ab2-ac2+4ac-4a;

214.x3n+y3n;

215.(x+y)3+125;

216.(3m-2n)3+(3m+2n)3;

217.x6(x2-y2)+y6(y2-x2);

218.8(x+y)3+1;

219.(a+b+c)3-a3-b3-c3;

220.x2+4xy+3y2;

221.x2+18x-144;

222.x4+2x2-8;

223.-m4+18m2-17;

224.x5-2x3-8x;

225.x8+19x5-216x2;

226.(x2-7x)2+10(x2-7x)-24;

227.5+7(a+1)-6(a+1)2;

228.(x2+x)(x2+x-1)-2;

229.x2+y2-x2y2-4xy-1;

230.(x-1)(x-2)(x-3)(x-4)-48;

231.x2-y2-x-y;

232.ax2-bx2-bx+ax-3a+3b;

233.m4+m2+1;

234.a2-b2+2ac+c2;

235.a3-ab2+a-b;

236.625b4-(a-b)4;

237.x6-y6+3x2y4-3x4y2;

238.x2+4xy+4y2-2x-4y-35;

239.m2-a2+4ab-4b2;

240.5m-5n-m2+2mn-n2.

参考答案:

三、因式分解:

1.(p-q)(m-1)(m+1).

8.(x-2b)(x-4a+2b).

11.4(2x-1)(2-x).

20.(x+3y)(x+y).

21.(x-6)(x+24).

27.(3+2a)(2-3a).

31.(x+y)(x-y-1).

38.(x+2y-7)(x+2y+5).

初三因式分解练习题及答案40题

因式分解3a3b2c-6a2b2c2+9ab2c3=3ab^2c(a^2-2ac+3c^2)因式分解xy+6-2x-3y=(x-3)(y-2)因式分解x2(x-y)+y2(y-x)=(x+y)(x-y)^2因式分解2x2-(a-2b)x-ab=(2x-a)(x+b)因式分解a4-9a2b2=a^2(a+3b)(a-3b)若已知x3+3x2-4含有x-1的因式,试分解x3+3x2-4=(x-1)(x+2)^2因式分解ab(x2-y2)+xy(a2-b2)=(ay+bx)(ax-by)因式分解(x+y)(a-b-c)+(x-y)(b+c-a)=2y(a-b-c)因式分解a2-a-b2-b=(a+b)(a-b-1)因式分解(3a-b)2-4(3a-b)(a+3b)+4(a+3b)2=[3a-b-2(a+3b)]^2=(a-7b)^2因式分解(a+3)2-6(a+3)=(a+3)(a-3)因式分解(x+1)2(x+2)-(x+1)(x+2)2=-(x+1)(x+2)abc+ab-4a=a(bc+b-4)16x2-81=(4x+9)(4x-9)9x2-30x+25=(3x-5)^2x2-7x-30=(x-10)(x+3)因式分解x2-25=(x+5)(x-5)因式分解x2-20x+100=(x-10)^2因式分解x2+4x+3=(x+1)(x+3)因式分解4x2-12x+5=(2x-1)(2x-5)3ax2-6ax=3ax(x-2)x(x+2)-x=x(x+1)x2-4x-ax+4a=(x-4)(x-a)25x2-49=(5x-9)(5x+9)36x2-60x+25=(6x-5)^24x2+12x+9=(2x+3)^2x2-9x+18=(x-3)(x-6)2x2-5x-3=(x-3)(2x+1)12x2-50x+8=2(6x-1)(x-4)因式分解(x+2)(x-3)+(x+2)(x+4)=(x+2)(2x-1)因式分解2ax2-3x+2ax-3=(x+1)(2ax-3)因式分解9x2-66x+121=(3x-11)^2因式分解8-2x2=2(2+x)(2-x)因式分解x2-x+14=整数内无法分解因式分解9x2-30x+25=(3x-5)^2因式分解-20x2+9x+20=(-4x+5)(5x+4)因式分解12x2-29x+15=(4x-3)(3x-5)因式分解36x2+39x+9=3(3x+1)(4x+3)因式分解21x2-31x-22=(21x+11)(x-2)因式分解9x4-35x2-4=(9x^2+1)(x+2)(x-2)因式分解(2x+1)(x+1)+(2x+1)(x-3)=2(x-1)(2x+1)因式分解2ax2-3x+2ax-3=(x+1)(2ax-3)因式分解x(y+2)-x-y-1=(x-1)(y+1)因式分解(x2-3x)+(x-3)2=(x-3)(2x-3)因式分解9x2-66x+121=(3x-11)^2因式分解8-2x2=2(2-x)(2+x)因式分解x4-1=(x-1)(x+1)(x^2+1)因式分解x2+4x-xy-2y+4=(x+2)(x-y+2)因式分解4x2-12x+5=(2x-1)(2x-5)因式分解21x2-31x-22=(21x+11)(x-2)因式分解4x2+4xy+y2-4x-2y-3=(2x+y-3)(2x+y+1)因式分解9x5-35x3-4x=x(9x^2+1)(x+2)(x-2)3x2-6x=3x(x-2)49x2-25=(7x+5)(7x-5)6x2-13x+5=(2x-1)(3x-5)x2+2-3x=(x-1)(x-2)12x2-23x-24=(3x-8)(4x+3)(x+6)(x-6)-(x-6)=(x-6)(x+5)3(x+2)(x-5)-(x+2)(x-3)=2(x-6)(x+2)9x2+42x+49=(3x+7)^2。x^2-x-2=(x-2)(x+1)x^2-x-6=(x-3)(x+2)2x^2-x-3=(2x-3)(x+1)5x^2-2x-7=(5x-7)(x+1)20x^2+9x-20=(5x-4)(4x+5)

初一因式分解练习题及答案

你可真狠要这么多题目

1.5ax+5bx+3ay+3by

解法:=5x(a+b)+3y(a+b)

=(5x+3y)(a+b)

2.x^3-x^2+x-1

解法:=(x^3-x^2)+(x-1)

=x^2(x-1)+(x-1)

=(x-1)(x^2+1)

3.x2-x-y2-y

解法:=(x2-y2)-(x+y)

=(x+y)(x-y)-(x+y)

=(x+y)(x-y-1)

bc(b+c)+ca(c-a)-ab(a+b)

=bc(c-a+a+b)+ca(c-a)-ab(a+b)

=bc(c-a)+bc(a+b)+ca(c-a)-ab(a+b)

=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)

=(bc+ca)(c-a)+(bc-ab)(a+b)

=c(c-a)(b+a)+b(a+b)(c-a)

=(c+b)(c-a)(a+b).

x^2+3x-40

=x^2+3x+2.25-42.25

=(x+1.5)^2-(6.5)^2

=(x+8)(x-5).

(x^2+x+1)(x^2+x+2)-12时,可以令y=x^2+x,则

原式=(y+1)(y+2)-12

=y^2+3y+2-12=y^2+3y-10

=(y+5)(y-2)

=(x^2+x+5)(x^2+x-2)

=(x^2+x+5)(x+2)(x-1).

(1+y)^2-2x^2(1+y^2)+x^4(1-y)^2

解:原式=(1+y)^2+2(1+y)x^2(1+y)+x^4(1-y)^2-2(1+y)x^2(1-y)-2x^2(1+y^2)

=[(1+y)+x^2(1-y)]^2-2(1+y)x^2(1-y)-2x^2(1+y^2)

=[(1+y)+x^2(1-y)]^2-(2x)^2

=[(1+y)+x^2(1-y)+2x]·[(1+y)+x^2(1-y)-2x]

=(x^2-x^2y+2x+y+1)(x^2-x^2y-2x+y+1)

=[(x+1)^2-y(x^2-1)][(x-1)^2-y(x^2-1)]

=(x+1)(x+1-xy+y)(x-1)(x-1-xy-y)

x^5+3x^4y-5x^3y^2+4xy^4+12y^5

解:原式=(x^5+3x^4y)-(5x^3y^2+15x^2y^3)+(4xy^4+12y^5)

=x^4(x+3y)-5x^2y^2(x+3y)+4y^4(x+3y)

=(x+3y)(x^4-5x^2y^2+4y^4)

=(x+3y)(x^2-4y^2)(x^2-y^2)

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

分解因式m+5n-mn-5m

解:m+5n-mn-5m=m-5m-mn+5n

=(m-5m)+(-mn+5n)

=m(m-5)-n(m-5)

=(m-5)(m-n)

分解因式bc(b+c)+ca(c-a)-ab(a+b)

解:bc(b+c)+ca(c-a)-ab(a+b)=bc(c-a+a+b)+ca(c-a)-ab(a+b)

=bc(c-a)+ca(c-a)+bc(a+b)-ab(a+b)

=c(c-a)(b+a)+b(a+b)(c-a)

=(c+b)(c-a)(a+b)

1.(2a-b)²+8ab

2.y²-2y-x²+1

3.x²-xy+yz-xz

4.6x²+5x-4

5.2a²-7ab+6b²

6.(x²-2x)²+2(x²-2x)+1

7.(x²-2x)²-14(x²-2x)-15

8.x²(x-y)+(y-x)

9.169(a+b)²-121(a-b)²

10.(x-3)(x-5)+1

答案:1.(2a-b)²+8ab=(2a+b)²

2.y²-2y-x²+1=(y-1)²-x²=(y-1-x)(y-1+x)

3.x²-xy+yz-xz=x(x-y)-z(x-y)=(x-z)(x-y)

4.6x²+5x-4=(2x-1)(3x+4)

5.2a²-7ab+6b²=(2a-3b)(a-2b)

6.(x²-2x)²+2(x²-2x)+1=(x²-2x+1)²=(x-1)^4

7.(x²-2x)²-14(x²-2x)-15=(x²-2x-15)(x²-2x+1)=(x+3)(x-5)(x-1)²

8.x²(x-y)+(y-x)=(x²-1)(x-y)=(x+1)(x-1)(x-y)

9.169(a+b)²-121(a-b)²

=(14a+14b-11a+11b)(14a+14b+11a-11b)

=(3a+25b)(25a+3b)

10.(x-3)(x-5)+1=(x-3)²-2(x-3)+1=(x-3-1)²=(x-4)²

-5a^2+16a=a(16-5a)

8x^2-4x=4x(2x-1)

15p+10p^2=5p(3+2p)

-3x^2y-6xy=-3xy(x+2y)

14m^3n^2-6m^2n^3=2m^2n^2(7m-6n)

27a^2b^3c+18ab^2=9ab^2(3abc+2)

18xy^2z^3+12x^2y^2=6xy^2(3z^3+2x)

8m^2n^2-6m^3n^2=2m^2n^2(4-3m)

因式分解3a3b2c-6a2b2c2+9ab2c3=3ab^2c(a^2-2ac+3c^2)

3.因式分解xy+6-2x-3y=(x-3)(y-2)

4.因式分解x2(x-y)+y2(y-x)=(x+y)(x-y)^2

5.因式分解2x2-(a-2b)x-ab=(2x-a)(x+b)

6.因式分解a4-9a2b2=a^2(a+3b)(a-3b)

7.若已知x3+3x2-4含有x-1的因式,试分解x3+3x2-4=(x-1)(x+2)^2

8.因式分解ab(x2-y2)+xy(a2-b2)=(ay+bx)(ax-by)

9.因式分解(x+y)(a-b-c)+(x-y)(b+c-a)=2y(a-b-c)

10.因式分解a2-a-b2-b=(a+b)(a-b-1)

11.因式分解(3a-b)2-4(3a-b)(a+3b)+4(a+3b)2=[3a-b-2(a+3b)]^2=(a-7b)^2

12.因式分解(a+3)2-6(a+3)=(a+3)(a-3)

13.因式分解(x+1)2(x+2)-(x+1)(x+2)2=-(x+1)(x+2)abc+ab-4a=a(bc+b-4)

(2)16x2-81=(4x+9)(4x-9)

(3)9x2-30x+25=(3x-5)^2

(4)x2-7x-30=(x-10)(x+3)

35.因式分解x2-25=(x+5)(x-5)

36.因式分解x2-20x+100=(x-10)^2

37.因式分解x2+4x+3=(x+1)(x+3)

38.因式分解4x2-12x+5=(2x-1)(2x-5)

39.因式分解下列各式:(1)3ax2-6ax=3ax(x-2)(2)x(x+2)-x=x(x+1)(3)x2-4x-ax+4a=(x-4)(x-a)(4)25x2-49=(5x-9)(5x+9)(5)36x2-60x+25=(6x-5)^2(6)4x2+12x+9=(2x+3)^2(7)x2-9x+18=(x-3)(x-6)(8)2x2-5x-3=(x-3)(2x+1)(9)12x2-50x+8=2(6x-1)(x-4)

40.因式分解(x+2)(x-3)+(x+2)(x+4)=(x+2)(2x-1)

41.因式分解2ax2-3x+2ax-3=(x+1)(2ax-3)

42.因式分解9x2-66x+121=(3x-11)^2

43.因式分解8-2x2=2(2+x)(2-x)

44.因式分解x2-x+14=整数内无法分解

45.因式分解9x2-30x+25=(3x-5)^2

46.因式分解-20x2+9x+20=(-4x+5)(5x+4)

47.因式分解12x2-29x+15=(4x-3)(3x-5)

48.因式分解36x2+39x+9=3(3x+1)(4x+3)

49.因式分解21x2-31x-22=(21x+11)(x-2)

50.因式分解9x4-35x2-4=(9x^2+1)(x+2)(x-2)

51.因式分解(2x+1)(x+1)+(2x+1)(x-3)=2(x-1)(2x+1)

52.因式分解2ax2-3x+2ax-3=(x+1)(2ax-3)

53.因式分解x(y+2)-x-y-1=(x-1)(y+1)

54.因式分解(x2-3x)+(x-3)2=(x-3)(2x-3)

55.因式分解9x2-66x+121=(3x-11)^2

56.因式分解8-2x2=2(2-x)(2+x)

57.因式分解x4-1=(x-1)(x+1)(x^2+1)

58.因式分解x2+4x-xy-2y+4=(x+2)(x-y+2)

59.因式分解4x2-12x+5=(2x-1)(2x-5)

60.因式分解21x2-31x-22=(21x+11)(x-2)

61.因式分解4x2+4xy+y2-4x-2y-3=(2x+y-3)(2x+y+1)

62.因式分解9x5-35x3-4x=x(9x^2+1)(x+2)(x-2)