(x十2y)(x一y)一2x(x一2y)因式分解，有哪位网友能够解答？

Question

如题所述

Answer 1

首先将每个括号内的项乘开：
(x十2y)(x一y) = x³ - x²y + 2xy² - 2y³
2x(x一2y) = 2x² - 4xy
现在将两个乘积相减，得到：
x³ - x²y + 2xy² - 2y³ - (2x² - 4xy)
= x³ - x²y + 2xy² - 2y³ - 2x² + 4xy
= x³ - x²y - 2x² + 2xy² + 4xy - 2y³
= x²(x - y) - 2y(x - y)(x + 2y)
= (x - y)(x² - 2y(x + 2y))
因此，原表达式可以写成两个因式的乘积：(x - y)(x² - 2y(x + 2y))。