Question

(a-b)^3-(a-b) 分解因式

a-b)^3-(a-b)
5a^2b(x-y)^3-30ab^2(y-x)^2
(x^2+y^2)^2-4x^2y^2
x^2-2xy+y^2-9
拜托各位、、分解因式 回答了加分啊....

Answer 1

(a-b)^3-(a-b)
=(a-b)[(a-b)^2-1]
=(a-b)(a-b+1)(a-b-1)

5a^2b(x-y)^3-30ab^2(y-x)^2
=5ab(x-y)^2[a(x-y)-6b]
=5ab(x-y)^2(ax-ay-6b)

(x^2+y^2)^2-4x^2y^2
=(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2

x^2-2xy+y^2-9
=(x-y)^2-3^2
=(x-y+3)(x-y-3)

追问

請問、4x^3y+4x^2y^2+xy^3 怎麼分解啊...

追答

4x^3y+4x^2y^2+xy^3
=xy(4x^2+4xy+y^2)
=xy(2x+y)^2

Answer 2

你顺序弄错了 分解因式是转化为积的形式原式=（a-b）【（a-b）^2 -1】=(a-b)(a-b+1)(a-b-1)