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 + 64

Accepted Answer

Welcome back. I am so glad you're here. We are asked to factories. The expression completely. Our expression is Q cubed or Q to the third power plus 1331. And our answer choices are answer choice. A parentheses, Q plus 11, close parentheses multiplied by open parentheses. Q squared minus 11, Q plus 121. Close parentheses. Answer choice B which is open parentheses, Q minus 11 closed parentheses multiplied by open parentheses. Q squared minus 11, Q plus 121 closed parentheses. Answer choice, C open parentheses. Q plus 11, close parentheses multiplied by open parentheses. Q squared plus 11, Q plus 121. Close parentheses and answer choice. D open parentheses, Q minus 11, close parentheses multiplied by open parentheses. Q squared plus 11, Q plus 121 closed parentheses. And so the first step in factoring, We want to look at our terms and ask ourselves if they share any common factors in between QQP or Q to the 3rd and 1331. They do not share any common factors. The next thing we ask ourselves when we have only two terms like this is if we're dealing with something like a difference of cubes or a difference of squares or sum of cubes. And in fact, we are dealing with that here, we've got this Q cubed or Q to the third power. And then that's plus 1331 is 11 cubed. So because we have two perfect cubes being added together, we have a sum of cubes and we could express this as open parentheses. A cubed plus B cubed, close parentheses. And then we know we can factor that as it's factored, it is open parentheses. A plus B closed parentheses multiplied by open parentheses. A squared minus A B plus B squared, close parentheses. Now it's just a matter of identifying our A and R B terms filling those into the factored some of cubes simplifying and then we have our answer. So are a term here. That's the first one being cute. That is Q, The B term. That's the second one being cubed. And here that is 11. So now we can fill in queue for A and 11 for B. So we have open parentheses instead of A Q plus instead of B 11 closed parentheses, multiplied by open parentheses. A squared, that's Q squared minus A times B, that's Q times 11 or 11 Q and then plus B squared and B is 11. So 11 squared, which is 121 closed parentheses. So here is our sum of cubes factored. We look at our answer choices for open parentheses. Q plus 11, close parentheses multiplied by open parentheses. Q squared minus 11, Q plus 121 close parentheses. And that matches with answer choice. A 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 + 64

Key Concepts

Sum of Cubes Formula

Identifying a and b

Factoring Polynomials

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