In Exercises 1–68, factor completely, or state that the polynomia...

Question

In Exercises 1–68, factor completely, or state that the polynomial is prime. x⁸ − y⁸

Accepted Answer

Perform complete factorization of the given expression or categorize it as the prime polynomial where we have into the eighth minus into the eighth. Some, we can make use of one of our exponent properties that states if we have X squared minus Y squared, the factors are X plus Y X minus Y like. So Now we can modify this into the 8th and into the 8th. You want to get to the fourth squared minus M to the fourth squared. Now that we have this, we can rewrite it in our form. This turns into M to the fourth plus N to the fourth times are multiplied by M to the 4th -M to the 4th like so now that we have this, we can look at M to the fourth minus N to the fourth because this follows the same principle. So if M into the fourth plus into the fourth multiplied by M to the second squared minus M to the second squared, which can be rewritten once again in our form to the fourth plus into the fourth, what's paid by M squared plus N squared times N squared minus and square like. So finally, we can check our M squared minus M squared, which we do have the form again To the 4th plus and into the 4th times M squared plus N squared multiplied by M plus N M minus N like, so we can't simplify this any further. So this turns out to be the answer to our problem. If you look over at our possible answers, we can determine the answer to our problem is answer C OK. Help to help you solve the problem. Thank you for watching. Goodbye.

In Exercises 1–68, factor completely, or state that the polynomial is prime. x⁸ − y⁸

Key Concepts

Difference of Squares

Factoring Polynomials

Prime Polynomials

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