Question

因式分解：①a(a-b)-b(b-a)②a^5-2a^4+a^3③a^4-3a^2-4④a^2-2ab+b^2-4

Answer 1

①a(a-b)-b(b-a)

=a(a-b)+b(a-b)

=(a-b)(a+b)

②a^5-2a^4+a^3

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

=a^2(a-1)^2

③a^4-3a^2-4

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

=(a-2)(a+2)(a^2+1)

④a^2-2ab+b^2-4

=(a-b)^2-4

=(a-b+2)(a-b-2)