问题 解答题

因式分

(1)x4-y4

(2)x3y-2x2y2+xy3

(3)4x2-4x+1 

(4)4(a-b)2+1+4(a-b)

答案

(1)x4-y4=(x2+y2)(x2-y2)=(x2+y2)(x+y)(x-y);

(2)x3y-2x2y2+xy3=xy(x2-2xy+y2)=xy(x-y)2

(3)4x2-4x+1=(2x-1)2

(4)4(a-b)2+1+4(a-b)=[2(a-b)+1]2=(2a-2b+1)2

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