Answer:
(x - 2y)³(1 - x+ 2y)(1 + x - 2y)
Step-by-step explanation:
Given
(x - 2y)³ - [tex](x-2y)^{5}[/tex] ← factor out (x - 2y)³ from both terms
= (x - 2y)³(1 - (x - 2y)²) ← difference of squares which factors in general as
a² - b² = (a - b)(a + b) , then
1 - (x - 2y)²
= 1² - (x - 2y)²
= (1 - (x - 2y) )(1 + (x - 2y) )
= (1 - x + 2y)(1 + x - 2y)
Then
(x - 2y)³ - [tex](x-2y)^{5}[/tex]
= (x - 2y)³(1 - x + 2y)(1 + x - 2y) ← in factored form
