因式分解习题.doc

因式分解练****题
 
(p-q)-p+q
141.(2m+3n)(2m-n)-4n(2m-n).
142.(x+2y)2-x2-2xy.
(ab+bc+ac)-abc.
-a-b+1.
-xy-xz+x-yz+y+z-1.
-2y4-2x3y+xy3.
(a2+b2+c2)-a3bc+2ab2c2.
149.(a-b-c)(a+b-c)-(b-c-a)(b+c-a).
(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.——————————————公式法
-c2a-ad2.
154.(x-y)2+12(y-x)z+36z2.
-4ax+8ab-4b2.
+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.
-48y4.
162.(x+1)2-9(x-1)2.
163.(x2+pq)2-(p+q)2x2.
164.(1+2xy)2-(x2+y2)2.
-(a2+b2)2.
-(a2+b2-c2)2.
167.(c2-a2-b2)2-4a2b2.
168.(x2-b2+y2-a2)2-4(ab-xy)2.
(x+1)2-49b4(x+1)4.
-ac2+4ac-4a.
-c2+6ab+3bc.
+y3n.
174.(x+y)3+125.
176.(m-n)6-(m+n)6.
177.(x+1)6-(x-1)6.
-b12.
179.(z-x)3-(y+z)3.
180.(3m-2n)3+(3m+2n)3.
(x2-y2)+y6(y2-x2).
(x+y)3+1.
183.(a-1)3-(b+1)3.
184.(a+b+c)3-a3-b3-c3.
+4xy+3y2.
-18xy+65.
+18x-144.
+30x+144.
+2x2-8.
+6x2-9.
191.-m4+18m2-17.
-7x2y2-20y4.
-2x3-8x.
-5a2b-300ab2.
+19x5-216x2.
+k-a2n+k-35ak.
+8xy-182y2.
+14m2-15.
答案
140.(p-q)(m-1)(m+1).
141.(2m-n)2.
(x+2y).
(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).
(b+c)2.
提示:原式=abc(a2+b2+c2-a2+2bc).
(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-