In Exercises 57–64, factor using the formula for the sum or diffe...

Question

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. 8x^3+125

Accepted Answer

Hello today we're gonna be factoring a given polynomial. So the polynomial given to us is 27 X cubed plus 64. Now looking at our 1st and 2nd term here, 27 X cubed is a perfectly cubed term because it could be rewritten as three X cubed and 64 is a cubed term because it could be rewritten as four cubed. So what we have here is a sum of cubed terms and we do have a special factory Ization for that. If we have um annoy real in the form of a cubed plus B cubed, this could be rewritten as a plus B times the quantity A squared minus a times B plus B squared. So what we're gonna do here is we're gonna let our a equal to the first cube term which is three X. And we're gonna let our be equal to the second cube term which is four. And we're gonna go ahead and plug this in to our factory ization so that we may be able to factor this some of cube terms. So plugging this in is going to give us a plus B or three X plus four times the quantity three X squared which is a squared minus a times B. Three x times four plus B squared which is four squared. And now we just need to go ahead and simplify a bit. So just gonna quickly write down three x plus four. The quantity three X squared evaluates to nine X squared three X times four is going to give us X. So that's gonna be minus 12 X. And four squared is going to be 16. And this is going to be the final Factory ization of our given polynomial. And that means that the answer to this problem is going to be D. So I hope this video helps you in understanding how to factor this kind of polynomial. And I'll go ahead and see you all in the next video.

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