In Exercises 75–94, factor using the formula for the sum or diffe...

Question

In Exercises 75–94, factor using the formula for the sum or difference of two cubes.

x³ − 27

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factories. The expression completely, the expression were given is R cubed minus 1728. Our answer choices are answer choice. A open parentheses are minus 12. Close parentheses multiplied by open parentheses. R squared minus 12, R plus 144. Close parentheses. Answer choice. B open parentheses are plus 12. Close parentheses multiplied by open parentheses. R squared minus 12, R plus 144. Close parentheses. Answer choice C open parentheses are minus 12. Close parentheses multiplied by open parentheses. R squared plus 12, R plus 144. Close parentheses and answer choice. D open parentheses are plus 12, close parentheses multiplied by open parentheses. R squared plus 12, R plus 144. Close parentheses are the first step in factoring is that we're going to look at all of our terms and see if they have any common factors that we can factor out between R cubed and 1728. Those don't share any common factors so nothing we can factor out in front. The next thing we want to ask ourselves when there are only two terms like that, we want to see if this is a difference of squares or a difference of cubes or is some of cubes. And that is what we're dealing with here. We have the R which is cubed and then minus. So this is a difference of and then that's 12 cubed. So we have to perfect cubes and they're being subtracted. We have a difference of cubes. And we recall from previous lessons that when we have a difference of cubes, which could be expressed as open parentheses. A cubed minus B cubed, close parentheses, we can factor this and that will be open parentheses. A minus B closed parentheses multiplied by open parentheses. A squared plus A B plus B squared, closed parentheses. Now we just have to identify our A and R B terms fill those in to our factor difference of cubes simplify and we've got our answer. So are a term, that's the first one that is being cubed are a term here is our In our B term. That's the second one. That's being cute. The B term here is 12. And so we can now fill in our for A and 12 for B. So this will be open parentheses instead of A, we have our minus instead of B, we have 12 close parentheses multiplied by open parentheses. Now for a square that's going to be R squared plus A times B that's going to be our times 12, which is 12 R plus B squared, that's 12 squared and 12 squared is 144. We can close parentheses and there is our difference of cubes factored. We look at our answer choices for open parentheses are minus 12, close parentheses multiplied by R squared plus 12, R plus 144 close parentheses. And that matches with answer choice. C well done. We'll catch you on the next one.

In Exercises 75–94, factor using the formula for the sum or difference of two cubes. x³ − 27

Key Concepts

Difference of Cubes

Factoring Techniques

Polynomial Expressions

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