Find each product. See Examples 5 and 6. [(9r-s)+2][(9r-s)-2]

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of the quantity of 11 x minus y plus six times the quantity of the quantity of x minus y minus six. Now taking a look at our given expression here, we can notice that we actually have the for factored out form of the difference of two squares. So with this in mind we need to recall the difference of two squares formula 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 we just want to compare the left hand side of our formula with our guy, give an expression to identify the values for A and B. So starting with our value for A. Well from our formula, we see that A is just the first term from both sets of parentheses here. So our first term from our expression is actually the quantity of 11 x minus y. So that's going to be our value for A. And now for our value for B. Well B is just going to be our second term. So in this case it is just going to be six. And now that we have identified the values for both A and B. We can go ahead and just substitute them into the right hand side of our formula. So again, originally we had the quantity of the quantity of x minus Y plus six times the quantity of the quantity of 11 x minus y minus six. And from our difference of squares formula we see that this expression is equivalent to the quantity of 11 x minus Y squared plus six. Or sorry not plus minus six squared. And so now we just have to start simplifying this expression and we can do this by squaring our six term here and also expanding out our first expression our first term. So doing this, we have the quantity of 11 X minus Y times the quantity of 11 x minus y minus six squared, which is just 36. So we have minus 36. And so now we see that we need to foil out our first two sets of parentheses here. So recalling the foil method, we first take the product of our first terms from both sets of parentheses which in this case we will have the quantity of X times the quantity of 11 X. And then we add our next product where we take our outside terms. So we have the quantity of 11 X times the quantity of now negative Y. And then again adding our next product. Where in this case we take the inside terms. So we have the quantity of negative Y times the quantity of 11 X. And now adding our last product here in the foil method where we take the last terms from both sets of parentheses. So we have the quantity of negative Y times the quantity of negative Y. And now we just have to bring down this minus 36 from earlier. And now our next step is to just start simplifying our foiled out expression here. So doing this 11 X times 11 X. Gives us 121 X squared. Then from our next product we get minus 11 X. Y. And then from our third product we get another minus 11 X. Y. And then from our fourth product of negative Y times negative Y gives us plus Y squared. And now again we just need to bring down this minus 36. So now our last step in simplifying is to just add together our like term here. And we see we end up with the final expression of X squared plus Y squared minus 22 X y minus 36. And with this we have found our fully multiplied out and simplified expression here which leaves us with answer choice D. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find each product. See Examples 5 and 6. [(9r-s)+2][(9r-s)-2]

Key Concepts

Factoring Difference of Squares

Distributive Property

Combining Like Terms

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