Find each product. See Examples 3–5. (2x+3)(2x-3)(4x^2-9)

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of four x plus five times the quantity of four x minus five times the quantity of 16 x squared minus 25. So now looking at our given expression here, before we begin multiplying terms together, we want to start by simplifying this expression and we can do this by applying the formula for the difference of two squares, which tells us that the quantity of A plus B times the quantity of a minus B is equivalent to a squared minus B squared. So now looking at our given expression, we see that our first two sets of parentheses here match the difference of squares formula. So we can go ahead and use this formula to simplify this portion of the expression. So doing this, we first need to identify the values for A and B. In relation to our expression. So starting with the value for A. Well from the formula we see that A is going to be the first time in both sets of parentheses. So A in our case is going to be four X. And now the other term is going to be the value for B. So B in our case is going to be five. So now with the A and B. Values identified, we can go ahead and use the right hand side of our formula to simplify our expression. So again recalling that our expression we had the quantity of four X plus five times the quantity of four x minus five. And now using our difference of squares formula we see that this expression is equivalent to the quantity of four X squared minus five squared. And now just simplifying this expression here that we found we have the expression of X squared minus 25. So now with this simplified expression we can go ahead and rewrite our original expression. So again our original given expression where we had the quantity of four X plus five times the quantity of four x minus five time. The quantity of 16 X squared minus 25. We can now rewrite this using our new information as the quantity of 16 X squared minus 25 times the quantity of 16 X squared minus 25. So now all that is left to do is to begin multiplying our terms together and we can do this using the foil method. And while using the foil method, we see that we first need to take the product of the first terms in both sets of parentheses. So we have the quantity of 16 X squared times the quantity of 16 X squared. And now we just need to add the next product where we take the outside terms. So we have plus the quantity of 16 X squared times the quantity of negative 25. And now adding the third product where we take the inside terms according to the foil method, we have the quantity of negative 25 times the quantity of 16 X squared. And now for our final products we have we take the last terms. So we have plus the quantity of negative 25 times the quantity of negative 25. So now all that is left to do is to start simplifying. So the first step in simplifying here we can just simplify these products. So from the first product we get 256 X. To the fourth power from our second product we minus 400 X. Squared. And our third product is the same as our second. So we get another minus 400 X. Squared. And from our last product we get plus 625. So now our last step in simplifying here is to just add together the like term. So doing this, we see our final answer here is X. To the fourth power minus 800 X squared plus 625. So with this we have found the full multiplication of our given expression here which leaves us with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time

Find each product. See Examples 3–5. (2x+3)(2x-3)(4x^2-9)

Key Concepts

Factoring

Polynomial Multiplication

Combining Like Terms

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