Find each product. See Example 5.

(2x + 5)³

Question

Find each product. See Example 5.

(2x + 5)³

Accepted Answer

Hey, everyone here we are asked to perform the indicated operations to simplify the given polynomial expression where we have the quantity of four P plus seven Q. Here we have four answer choice options, answer choice. A 64 P cubed plus 336 P squared plus 588 P plus 343. Then we have answer choice B 64 P cubed plus 84 P plus 343. Answer C 64 P cubed plus 84 P squared plus P plus 343. And lastly answer D 64 P cubed plus 343. So to begin simplifying our given polynomial expression, we first need to recall the formula where we have the quantity of X plus Y cubed is equivalent to X cubed plus three, X squared multiplied by Y plus three, X multiplied by Y squared plus YQ. Now, we just want to compare the left side of our formula to our given expression to identify the values for X and Y. So starting with X, we see the first term in our expression is four P. So we know X is going to be four P that tells us that Y is going to be seven. And now with our X and Y identified, we can begin finding our terms that are on the right side of our formula. So we can start with X cubed. Well, X cubed just gives us the quantity of four P cubed. And now simplifying the quantity of four P cubed gives us 64 P cubed. Now moving on X squared gives us the quantity of four P squared and then simplifies to 16 P squared. Then we have, we can move on to our Y terms. So we have Y squared which gives us seven squared and seven squared simplifies 2 49. Then we have YQ which gives us seven Q and this value simplifies to 343. So now with all of our X and Y terms identified, we can begin substituting in their values into the right side of our formula. So, so far we have the quantity of four P plus seven P is equivalent to X cubed, which we identified as 64 P cubed. We then have plus three multiplied by 16 P squared multiplied by seven. Then we have plus three multiplied by four P multiplied by 49. And lastly, we have plus 343. So now all that is left to do in simplifying is just perform the necessary multiplication in our expression. So far. So multiplying we get 64 P cubed plus 336 P squared plus 588 P plus 343. So now looking at our final expression, we see that there are no further simplifications that we can make. So we are left with answer choice. A where again, our simplified expression is 64 PQ plus 336 P squared plus 588 P plus 343. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find each product. See Example 5. (2x + 5)³

Key Concepts

Binomial Theorem

Polynomial Expansion

Coefficients and Combinations

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