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^3−27

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Hello Today we're going to be factoring a summer difference of cube numbers. And when we are trying to factor a summer difference of Q numbers we have two general rules to work with. We have a cubed plus B cubed can be factored to a plus B times a squared minus A times B plus b squared. And the other general rule for factoring a difference of cubes is a cubed minus B cubed is equal to a minus B times the quantity A squared plus A B plus B squared. Now, depending on which one you need to use really depends on what is given to us. However, notice that there is a clear difference in the pattern of the signs for both of the rules. So when you're trying to factor of some of cubes, the pattern for the signs is plus minus plus. And when you are trying to factor a difference of cubes, the pattern is minus plus plus. So essentially what's going on with these two is that the first two signs are just opposite of each other. A sum has plus minus for its beginning signs and the difference has minus plus. So just keep that in mind. When you're trying to factor Okay now let's go ahead and take a look at the given expression we are given X cubed minus 64. And since we are given a difference of cube terms we want to go ahead and use the general rule for factoring a difference of cubes. Now X cubed can be rewritten as X times itself three times. So this can be X to the power of three and can be rewritten as four times itself three times. So 64 can be represented as four to the power of three. So here we can allow A to B X and B two B four. And now we just need to go ahead and take these values and plug into our general rule of factoring a some a difference of cubes and that's going to be a minus B which is x minus four times the quantity A squared which is X squared plus A times B which is X times four plus B squared, which is four squared. Now at four times X is just going to give us for X and four squared can be rewritten as 16. So simplifying this is going to give us x minus four times the quantity X squared plus four X plus 16. And this is going to be the completely factored version of our given expression. And that means that the answer to this problem is going to be C. So I hope this video helps you in understanding how to factor a difference of cubes. And I'll go ahead and see you all in the next video

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. x^3−27

Key Concepts

Difference of Cubes

Factoring Techniques

Polynomial Expressions

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