Question

分解因式 (a^2-a)^2-(a-1)^2

Answer 1

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

追问

我知道了,应当是(a+1)(a-1)^2

Answer 2

(a+1)(a-1)^3

Answer 3

原式=a^4-a^2-(a^2-1)
=a^4-a^2-a^2+1
=a^4-2a^2+1
=(a^2-1）^2
……………………………………………………