把下列各式分解因式: (1)x6-81x2y4 | (2)2x2-x-3 |
(3)x2-7x-8 | (4)a3-2a2+a |
(5)a2+6a+5 | (6)7x2+13x-2 |
(7)-x2+4x+5 | (8)-3x2+10x+8 |
(9)x3z-4x2yz+4xy2z | (10)x3z-4x2yz+4xy2z |
(11)x4+6x2+9 | (12)(x-1)2-4(x-1)y+4y2 |
(13)(x2-10)(x2+5)+54 | (14)(a-b)(x-y)-(b-a)(x+y) |
(15)4m5+8m3n2+4mn4 | (16)4a2+4ab+b2-1 |
(17)x3-x2-2x+2. |
(1)x6-81x2y4,
=x2(x4-81y4),
=x2(x2+9y2)(x2-9y2),
=x2(x2+9y2)(x+3y)(x-3y);
(2)2x2-x-3=(2x-3)(x+1);
(3)x2-7x-8=(x+1)(x-8);
(4)a3-2a2+a,
=a(a2-2a+1),
=a(a-1)2;
(5)a2+6a+5=(a+1)(a+5);
(6)7x2+13x-2=(7x+1)(x-2);
(7)-x2+4x+5
=-(x2-4x-5),
=-(x+1)(x-5);
(8)-3x2+10x+8,
=-(3x2-10x-8),
=-(3x+2)(x-4);
(9)x3z-4x2yz+4xy2z,
=xz(x2-4xy+4y2),
=xz(x-2y)2;
(10)x3z-4x2yz+4xy2z,
=xz(x2-4xy+4y2),
=xz(x-2y)2;
(11)x4+6x2+9=(x+3)2;
(12)(x-1)2-4(x-1)y+4y2=(x-1-2y)2;
(13)(x2-10)(x2+5)+54,
=x4-5x2-50+54,
=x4-5x2+4,
=(x2-1)(x2-4),
=(x+1)(x-1)(x+2)(x-2);
(14)(a-b)(x-y)-(b-a)(x+y),
=(a-b)(x-y+x+y),
=2x(a-b);
(15)4m5+8m3n2+4mn4,
=4m(m4+2m2n2+4n4),
=4m(m2+n2)2;
(16)4a2+4ab+b2-1,
=(4a2+4ab+b2)-1,
=(2a+b)2-1,
=(2a+b+1)(2a+b-1);
(17)x3-x2-2x+2,
=(x3-x2)-(2x-2),
=x2(x-1)-2(x-1),
=(x-1)(x2-2).
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