问题
解答题
分解因式.
(1)a2+b2-2ab-1;
(2)(2x+y)2-(x-2y)2;
(3)(a+b)2-6(a+b)+9;
(4)-4(m+n)2+25(m-2n)2.
答案
(1)a2+b2-2ab-1,
=(a2+b2-2ab)-1,
=(a-b)2-1,
=(a-b+1)(a-b-1);
(2)(2x+y)2-(x-2y)2,
=(2x+y+x-2y)(2x+y-x+2y),
=(3x-y)(x+3y);
(3)(a+b)2-6(a+b)+9=(a+b-3)2;
(4)-4(m+n)2+25(m-2n)2,
=25(m-2n)2-4(m+n)2,
=(5m-10n+2m+2n)(5m-10n-2m-2n),
=3(7m-8n)(m-4n).