Find each product. See Examples 3–5. (x+1)(x+1)(x-1)(x-1)

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of a plus two times the quantity of a plus two times the quantity of a minus two times the quantity of a minus two. Now we want to start solving this problem by first simplifying our given expression rather than multiplying right away to make the this multiplication process easier. So to simplify this expression, we just need to recall the difference of two squares formula, which tells us that the quantity of X plus y times the quantity of x minus y is equal to x squared minus y squared. So now our next step is to just rewrite our given expression to better match our formula. So doing this, our original expression becomes the quantity of a plus two times the quantity of a minus two times the quantity of a plus two times the quantity of a minus two. So now looking at our rewritten expression, we can see that we actually have two sets of the difference of square formula here. But since they are both the same terms in both parts of the expression, we only need to find the simplified form of one of the expressions. So doing this, we first need to identify the values for X and Y in relation to our expression here. So our value for X is the first term in each set parentheses. So X is just going to be A and then our other term is going to be the value for Y. So why is just going to be too. So now we can see that the expression of the quantity of a plus two times the quantity of a minus two according to our formula, this expression is equivalent to a squared minus two squared. And now simplifying, we see that our expression simplifies to a squared minus four. So now that we have found this simplified expression, we can apply it to our original given expression and so are our original expression. Again, we had the quantity of a plus two times the quantity of a minus two times the quantity of a plus two times the quantity of a minus two. While simplifying this expression by utilizing what we found with the difference of squares. Formula, we can rewrite this expression as the quantity of a squared minus four times the quantity of a squared minus four. And now our next step is to actually start multiplying our terms together here and we can do this by utilizing the foil method. Well, the foil method tells us to begin by taking the product of the first terms in each set of parentheses. So we first have the quantity of a squared times the quantity of a squared. And now we add our next product. And according to the foil method, we take the product of the outside terms. Now, so we have plus the quantity of a squared times the quantity of negative four. And for our next product we take the inside terms. So we have plus the quantity of negative four times the quantity of a squared. And now for our last product we take the product of our last terms. So doing this we have plus the quantity of negative four times the quantity of negative four. So now all that is left to do is to start simplifying and we can begin by simplifying each of our products here. So doing this. Our first product gives us A to the fourth power. And then from our next product we get minus for a squared. And our third product is the same as our second product. So we have minus another for a squared. And lastly from our last Prada we have plus 16. So now we just have to finish simplifying by adding together the like terms. And we see we have a final answer of A. To the fourth power minus eight A squared plus 16. And with this we have fully finished multiplying our original given expression. Therefore we are left with answer choice B. 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. (x+1)(x+1)(x-1)(x-1)

Key Concepts

Polynomial Multiplication

Factoring and Special Products

Combining Like Terms

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