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

Algebra factoring

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Jack M. | Keys to Chemistry, Calculus, Literature and MoreKeys to Chemistry, Calculus, Literature...
4.7 4.7 (309 lesson ratings) (309)

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).

Removing it from both terms leaves:

     (x - 2y)[ 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)]