變號法則與提公因式

變號法則：

★ $(x-1)=-(1-x)$

★ $(x-1)^2=(1-x)^2$

例 因式分解下列各式：

1. $x(x-3)-(3-x)(2-x)$
2. $a(x-y)-(y-x)^2$

解

1. $\begin{array} {rl} & x(x-3)-(3-x)(2-x) \\ = & x(x-3)-[-(x-3)](2-x) \\ = & x(x-3)+(x-3)(2-x) \\ = & (x-3)[x+(2-x)] \\ = & (x-3)(x+2-x) \\ = & 2(x-3) \end{array}$
2. $\begin{array} {rl} & a(x-y)-(y-x)^2 \\ = & a(x-y)-(x-y)^2 \\ = & (x-y)[a-(x-y)] \\ = & (x-y)(a-x+y) \end{array}$