Find each product. See Example 5.

(5r - 3t²)²

Question

Find each product. See Example 5.

(5r - 3t²)²

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 minus 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 minus 49 Y squared and answer D 49 K squared minus 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 minus Y squared is equivalent to X squared minus two XY plus Y squared. Now, we just want to compare the left side of our formula with our given expression to determine our values for X and Y. So our positive term in the given expression is seven K. So this tells us that X is going to be seven K and that means Y is going to be three Y. And now with our X and Y terms identified, we can begin finding the terms on the right side of our formula. So, starting with X squared, we get the quantity of seven k squared and this simplifies 2 49 k squared. We then have Y squared. Well, Y squared 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 the information we have gathered so far into our formula. And so we have the quantity of seven K minus three Y squared. And this is now equivalent to X squared, which we found to be 49 K squared. We then have minus two multiplied by seven K multiplied by three Y. And lastly, we just have plus nine Y squared. So now to finish simplifying, we just need to perform the necessary multiplication. And so our expression becomes 49 K squared minus 42 ky plus nine Y squared. And now with our final expression, we see that there is no further simplifications that we can make. And so we are left with answer choice. A where again our simplified expression is 49 K squared minus 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. (5r - 3t²)²

Key Concepts

Binomial Expansion

Algebraic Manipulation

Like Terms

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