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

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Expanding (x - a)^4 is not necessary for factoring the expression 64(x - a)^4 - x + a. The initial step involves rewriting the expression as 64(x - a)^4 - (x - a). By factoring out (x - a), the remaining factor can be identified as a difference of cubes. This approach simplifies the factoring process without the need for expansion. The discussion emphasizes efficient strategies for factoring polynomials.
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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.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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