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将下列各式因式分解:(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)
题目详情
将下列各式因式分解:
(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.
(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.
▼优质解答
答案和解析
(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).
(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).
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