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. x^3+64

Accepted Answer

Hello today we're going to be factoring a given polynomial. So the polynomial given to us is X cubed plus 125. Now, if we take a look at both of these terms, both of these terms are perfect cubes. X cubed could be rewritten as X raised to the third power and 100 and 25 can be rewritten as five raised to the third power. So what we have here is a sum of cubed terms and we have a special special factory Ization for that. What that is is a cubed plus B cubed can be factored as A plus B times a squared minus a times B plus B squared. Now, in order to use this, we need to go ahead and identify what are A and B are going to be Well, R A is just going to be the first cube term which is going to be X. So A is equal to X and B is our second cube term. So B is going to equal to five. Now what we need to do is go ahead and plug those values into our factory ization in order to factor given polynomial. So plugging that in, we're going to get a plus B or X plus five times a squared which is x squared minus a times B which is x times five plus B squared which is five squared. Now, what we need to do is go ahead and simplify this right hand quantity. So Rewriting X plus five, X squared is just gonna be X squared X times five is going to give us five X. So we have minus five X. And five squared is going to give us 25 so that's gonna be plus 25. And this is going to be the final factory ization of our given polynomial. And the answer to this problem is going to be be So I hope this video helps you in understanding how to factor this type of polynomial. And I'll go ahead and see you all in the next video.

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