问题 解答题
把下列各式分解因式:
(1)-
m2
9
-1+
2m
3

(2)
1
2
p2-2pq

(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)-

m2
9
-1+
2m
3
=-
1
9
(m2+9-6m)=-
1
9
(m-3)2

(2)

1
2
p2-2pq=
1
2
p(p-4q)

(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).

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