因式分解三題

Question

利用分組,因式分解下列各式
Q1:
(x-1)^2+3x-3
Q2:
(ax-bx)^2-(a-b)x^3
Q3:
a^2b(x^2-xy)+ab^2(y^2-xy)

Answer 1

Q1:(x-1)2+3x-3=(x-1)2+3(x-1)=(x-1)(x-1+3)=(x-1)(x+2)Q2:(ax-bx)2-(a-b)x3=x2(a-b)2-(a-b)x3=x2(a-b)(a-b-x)Q3:a2b(x2-xy)+ab2(y2-xy)=(a2b)x(x-y)+(ab2)y(y-x)=(a2b)x(x-y)-(ab2)y(x-y)=ab(x-y)(ax)-ab(x-y)(by)=ab(x-y)(ax-by)