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题目
分解因式:
(1)(2x2-3x+1)2-22x2+33x-1;
(2)x4+7x3+14x2+7x+1;
(3)(x+y)3+2xy(1-x-y)-1;
(4)(x+3)(x2-1)(x+5)-20.

提问时间:2021-01-15

答案
(1)(2x2-3x+1)2-22x2+33x-1,
=(2x2-3x+1)2-11(2x2-3x+1)+10,
=(2x2-3x+1-1)(2x2-3x+1-10),
=(2x2-3x)(2x2-3x-9),
=x(2x-3)(2x+3)(x-3);
(2)x4+7x3+14x2+7x+1,
=x4+4x3+6x2+4x+1+3x3+6x2+3x+2x2
=[(x+1)2]2+3x(x+1)2+2x2
=[(x+1)2+2x][(x+1)2+x],
=(x2+4x+1)(x2+3x+1);
(3)(x+y)3+2xy(1-x-y)-1
=[(x+y)3-1]+2xy(1-x-y)
=(x+y-1)[(x+y)2+x+y+1]-2xy(x+y-1)
=(x+y-1)(x2+y2+x+y+1);
(4)(x+3)(x2-1)(x+5)-20,
=(x+3)(x+1)(x-1)(x+5)-20,
=(x2+4x+3)(x2+4x-5)-20,
=(x2+4x)2-2(x2+4x)-15-20,
=(x2+4x+5)(x2+4x-7).
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