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).

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