Question

分解因式,三题(1)a4-a3+a2-a(2)4a2-9b2+c2-4ac(3)(ax+by)2(bx-ay)2要求：使

Answer 1

(1)a^4-a^3+a^2-a

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

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

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

(2)4a^2-9b^2+c^2-4ac

=(4a^2-4ac+c^2)-9b^2

=(2a-c)^2-(3b)^2

=(2a-c+3b)(2a-c-3b)

(3)(ax+by)^2+(bx-ay)^2

=(ax)^2+2abxy+(by)^2+(bx)^2-2abxy+(ay)^2

=(a^2+b^2)(x^2+y^2)