Find each product. See Example 5. (4x² - 5y) (4x² + 5y)

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 nine K squared minus seven X multiplied by the quantity of nine K squared plus seven X. Here we have four answer choice options, answer choice. A 49 K race to the fourth power minus 81 X squared. Answer B 81 K raised to the fourth power minus 49 X squared. Answer C 81 K raised to the fourth power minus XK squared minus 49 X squared. Answer D 81 K raised to the fourth power minus 126 XK squared plus 49 X squared. So to begin simplifying our given expression, we first need to recall the difference of squares formula which states that the quantity of X plus Y multiplied by the quantity of X minus Y is equivalent to X squared minus Y squared. So now we just want to compare the left side of our formula with our given polynomial expression so that we can identify our values for X and Y. So here we can see that the first term in both sets of parentheses in our given expression is nine k squared. So this tells us that X is going to be nine k squared and that means Y is going to be seven X. So now we can start finding the values of X squared and Y squared on the right side of our formula. So beginning with X squared, we have the quantity of nine k squared and this quantity is squared. So simplifying we get 81 K raised to the fourth power. And now we all we have left is Y squared and Y squared gives us the quantity of seven X squared. And this simplifies to 49 X squared. So now just substituting in all of our values into our formula, we find that the quantity of nine K squared minus seven X multiplied by the quantity of nine K squared plus seven X is equivalent to X squared, which we found to be 81 K squared minus Y squared, which is equivalent to 49 X squared. So now with our final expression, we see that there are no further simplifications that we need to make. So we are left here with answer choice B where again, our final expression is 81 K race to the fourth power minus 49 X 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. (4x² - 5y) (4x² + 5y)

Key Concepts

Difference of Squares

Polynomial Multiplication

Exponents and Like Terms

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