Find each product. See Example 5. (4m + 2n)²

Question

Accepted Answer

Hey, everyone here, we are asked to perform the indicated operations to simplify the given expression where we have the quantity of seven K plus three Y squared. Here we have four answer choice options, answer choice. A 49 K squared minus ky plus nine Y squared. Answer B 49 K squared plus 42 ky plus nine Y squared. Answer C nine K squared plus Y squared and answer D K squared plus nine Y squared. So to begin simplifying our given polynomial expression, we first need to recall the formula which states that the quantity of X plus Y squared is equivalent to X squared plus two XY plus Y squared. So now we just want to compare the left side of our formula to our given expression. Since we can see that they follow the same format and doing this, we can find our values for X and Y. So starting with X, we see the first term in our expression is seven K. So X is just going to be seven K and then we will have YB three Y. And so now we just want to start finding our terms on the right side of the formula. So we have X squared, which gives us the quantity of seven k squared. And this simplifies 2 49 k squared. We then have Y squared which gives us the quantity of three Y squared. And this simplifies 29 Y squared. And so now we can just start substituting in all of our information that we have found so far into our formula. So we have the quantity of seven K plus three Y squared. And this is equivalent to X squared, which we found to be 49 K squared. We then have plus two multiplied by seven K multiplied by three Y. And lastly, we have plus nine Y squared. And so now the last step in simplifying is to just perform the necessary multiplications. So we have our expression becomes 49 K squared plus 42 ky plus nine Y squared. And now looking at our current expression, we see that there is no further simplifications that we can make. So we are left with answer choice B where again, our simplified expression is 49 K squared plus 42 ky plus nine Y squared. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find each product. See Example 5. (4m + 2n)²

Key Concepts

Binomial Expansion

Distributive Property

Combining Like Terms

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