简介:[方法一]提取公因式法例1分解因式:5(x-y)~3—45(y-x)~2-20(y-x)解:原式=5(x-y)~3-45(x-y)~2+20(x-y)=5(x-y)[(x-y)~2-9(x-y)+20]=5(x-y)(x-y-4)(x-y-5)[方法二]公式分解法例2分解因式:(a-b)~3+(b-c)~3+(c-d)~3解:原式=(a-b)~3+(b-c)~3+[(c-b)+(b-a)]~3=(a-b)~3+(b-c)~3-[(b-c)+(d-b)]~3=(a-b)~3+(b-c)~3-(b-c)~3-3(b-c)~2(a-b)-3(b-c)(a-b)~2-(a-b)~3=-3(b-c)~2(a-b)-3(b-c)(a-b)~2=-3(a-b)(b-c)[(b-c)+(a-b)]=-3(a-b)(b-c)(c-a)=3(a-b)(b-c)(c-a)。