因式分解

Question

(1). x的平方-2xy+y的平方+2x-2y+1 (2).(x-m)的立方(x-n)+(x-m)的平方(n-x)

Answer 1

解：
(1). x的平方-2xy+y的平方+2x-2y+1
=(x-y)的平方+2(x-y)+1
=(x-y+1)的平方

(2).(x-m)的立方(x-n)+(x-m)的平方(n-x)
=(x-m)的立方(x-n)-(x-m)的平方(x-n)
=(x-m)的平方(x-n)(x-m-1)

Answer 2

解:
(1). x²-2xy+y²+2x-2y+1
=(x-y)²+2(x-y)+1
=(x-y+1)²

(2). (x-m)³(x-n)+(x-m)²(n-x)

= (x-m)³(x-n)-(x-m)²(x-n)
=(x-m)²(x-n)(x-m-1)

Answer 3

先观察，再归类
解:
(1). x²-2xy+y²+2x-2y+1
=(x-y)²+2(x-y)+1
=(x-y+1)² (2). (x-m)³(x-n)+(x-m)²(n-x)
= (x-m)³(x-n)-(x-m)²(x-n)

=(x-m)²(x-n)(x-m-1)