问题
解答题
把下列各式分解因式: (1)-
(2)
(3)a2(a-3)-a+3 (4)2xy-x2-y2+1 (5)(m-n)3+(n-m)m2 (6)4(x+2y)2-25(x-y)2 |
答案
(1)-
-1+m2 9
=-2m 3
(m2+9-6m)=-1 9
(m-3)2;1 9
(2)
p2-2pq=1 2
p(p-4q);1 2
(3)a2(a-3)-a+3=a2(a-3)-(a-3)=(a-3)(a2-1)=(a-3)(a+1)(a-1);
(4)2xy-x2-y2+1=1-(x2-2xy+y2)=1-(x-y)2=(1+x-y)(1-x+y)
(5)(m-n)3+(n-m)m2=(m-n)3-(m-n)m2=(m-n)[(m-n)2-m2]=n(m-n)(n-2m)
(6)4(x+2y)2-25(x-y)2=[2(x+2y)+5(x-y)][2(x+2y)-5(x-y)]=(7x-y)(9y-3x)
=3(7x-y)(3y-x).