Algebra factoring

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

Tutors, please sign in to answer this question.

# 1 Answer

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)]**