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

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 23 T plus four multiplied by the quantity of 23 T minus four. Here we have four answer choice options, answer choice, A 529 T squared minus 16. Answer B 459 T squared minus 16 answers C 529 T squared minus 184 T plus and answer D 459 T squared minus 184 T plus 16. So to begin simplifying our given polynomial 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 expression to find our values for X and Y. So starting with our value for X. Well, we can see that the first term in both sets of parentheses in our given expression is 23 T So this tells us that X is equivalent to 23 T and that means Y is equivalent to four. So now with our X and Y variables identified, we want to now start finding the terms on the right side of the formula where we have X squared and Y squared. So starting with X squared, we get the quantity of 23 T squared. And now simplifying we have T squared. Now moving on to Y squared, well, Y squared gives us the quantity of four squared and simplifying we get 16. So now we just want to substitute in all of the information we have found so far into our formula. And so we have the quantity of T plus four multiplied by the quantity of 23 T minus four. And this is equivalent to 529 T squared minus 16. And now looking at our simplified expression, we can see that there are no further simplifications that we need to make. And so we are left here with answer choice. A where again, our simplified expression is T squared minus 16. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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

Key Concepts

Difference of Squares

Binomial Multiplication

Polynomial Simplification

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