【求完整回答及說明】中二數學題恆等式兩條

這兩題應是因式分解的題目吧！


1.
解一：
設 u = x + 2
則 5(x + 2)² - 15(x + 2)
= 5u² - 15u
= 5u(u - 3)
= 5(x + 2) [(x + 2) - 3]
= 5(x + 2)(x + 2 - 3)
= 5(x + 2)(x - 1)

解二：
5(x + 2)² - 15(x + 2)
= 5(x + 2) [(x + 2) - 3]
= 5(x + 2)(x + 2 - 3)
= 5(x + 2)(x - 1)


2:
解一：
設 u = x + y - 1
則 (x + y - 1)² - 4(x + y -1)
= u² - 4u
= u(u - 4)
= (x + y - 1) [(x + y - 1) - 4]
= (x + y - 1)(x + y - 1 - 4)
= (x + y - 1)(x + y - 5)

解二：
(x + y - 1)² - 4(x + y -1)
= (x + y - 1) [(x + y - 1) - 4]
= (x + y - 1)(x + y - 1 - 4)
= (x + y - 1)(x + y - 5)