(x-2y)^3 -(x-2y)^5

Question

Algebra factoring

Answer 1

The form of the final answer depends on how far you want to take the factoring.

The first step is to find the largest factor common to both terms: (x - 2y)³ .

Removing it from both terms leaves:

     (x - 2y)³ [ 1 - (x - 2y)² ]

The second term is the difference of two squares, 1 and (x - 2y)² . It can be factored as:

     [ 1 + (x - 2y)] [1 - (x - 2y)]

The interior parentheses could be removed by distributing the + and - signs across the (x - 2y) terms, but that would not simplify it much. Neither would multiplying it out.

I would suggest this as the final answer:

     (x - 2y)³ [1 + (x - 2y)] [1 - (x + 2y)]