Is Expanding (x - a)^4 Necessary for Factoring 64(x - a)^4 - x + a?

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The discussion centers on the necessity of expanding the expression 64(x - a)4 - x + a for factoring. A participant suggests that instead of expanding, one can rewrite the expression as 64(x - a)4 - (x - a) and then factor out (x - a). This approach leads to identifying the remaining factor as a difference of cubes, simplifying the factoring process without the need for expansion.

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mathdad
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Factor: 64(x - a)^4 - x + a

Must I expand (x - a)^4 as step 1?
 
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As a first step, I would write:

$$64(x-a)^4-x+a=64(x-a)^4-(x-a)$$

Next factor out $x-a$, and the other factor will be the difference of cubes. :D
 
I can take it from here.
 

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