将下列各式因式分(1)a3-16a; (2)4ab+1-a2-4b2.(3)9(a-b)2+12(a2-b2)+4(a+b)
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将下列各式因式分 (1)a3-16a; (2)4ab+1-a2-4b2. (3)9(a-b)2+12(a2-b2)+4(a+b)2; (4)x2-2xy+y2+2x-2y+1. (5)(x2-2x)2+2x2-4x+1. (6)49(x-y)2-25(x+y)2 (7)81x5y5-16xy (8)(x2-5x)2-36. |
答案
(1)a3-16a=a(a2-16)=a(a+4)(a-4); (2)4ab+1-a2-4b2=1-(-4ab+a2+4b2)=1-(a-2b)2=(1+a-2b)(1-a+2b);
(3)9(a-b)2+12(a2-b2)+4(a+b)2=[3(a-b)]2+2×3(a-b)×2(a+b)+[2(a+b)]2=[3(a-b)+2(a+b)]2=(5a-b)2;
(4)x2-2xy+y2+2x-2y+1=(x-y)2+2(x-y)+1=(x-y+1)2;
(5)(x2-2x)2+2x2-4x+1=(x2-2x)2+2(x2-2x)+1=(x2-2x+1)2=(x-1)4;
(6)49(x-y)2-25(x+y)2=[7(x-y)]2-[5(x+y)]2=[7(x-y)+5(x+y)][7(x-y)-5(x+y)]=(12x-2y)(2x-12y)=4(6x-y)(x-6y);
(7)81x5y5-16xy=xy(81x4y4-16)=xy(9x2y2+4)(9x2y2-4)=xy(9x2y2+4)(3xy+2)(3xy-2);
(8)(x2-5x)2-36=(x2-5x+6)(x2-5x-6)=(x-2)(x-3)(x-6)(x+1). |
举一反三
已知a-b=2005,ab=,求a2b-ab2的值. |
把下列各式分解因式 (1)12a3b2-9a2b+3ab; (2)9x2-4y2; (3)x2(x-y)+(y-x); (4)(x-1)2+10(x-1)+25. |
分解因式: (1)8a3b2-12ab3c+4abc (2)(x2-2x)2-1. |
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