Find each product. See Examples 5 and 6. [(2m+7)-n]^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 16 P plus 17 minus Q squared. So now our first step here in solving this problem is to just expand our given expression here. So doing this, we have the quantity of the quantity of 16 P plus 17 minus Q. Times the quantity of the quantity of 16 P plus 17 minus Q. And so now that we have fully expanded our given expression, we can now start multiplying terms together by applying the foil method. So recalling the foil method, we first take the product of the first terms in both sets of parentheses here. So we have the quantity of 16 P plus times the quantity of 16 P plus 17 plus our net next product here which again according to the foil method, we now take the outside terms. So we have the quantity of 16 P plus times the quantity of negative Q. And then again we add our next product here which in this case we take the inside terms. So we have the quantity of negative Q times the quantity of 16 P. Plus 17. And now we add add our last product here where we take the last terms from both sets of parentheses. So we have the quantity of negative Q. Times the quantity of negative Q. And so now all that is left to do is to start simplifying our fully foiled out expression here. So doing this, looking at our first product, we see that we have to foil out this expression again. So doing this we have 16 p. Times 16 p plus p. times 17 plus 17 times 16 P plus 17 times 17. And now for our second product here we just have to distribute the negative Q. So we have negative Q. Times 16 P. Plus negative Q. Times 17. And then our third product we do the same thing and just distribute the negative Q. So we again have minus Q. Times 16 P minus Q. Times 17. And for our last product here we have a negative Q. Times negative Q. Which just gives us plus Q squared. And so now we just have to continue to simplify this expression here. So from our first product we get 200 and 56 P squared. And then from 16 p. Times 17 we get plus 272 P. And then we have another plus 272 P. And then from our 17 squared here we have plus 289. And now from our next term our negative Q. Times 16 P. We get or minus 16 P. Q. And then we have After -16 p. Q. We have -17q. Then we have another minus another minus 16 P. Q. Then we have another minus 17 Q. And lastly we just have plus Q squared. And so now we have finished multiplying out all of our terms. So now we just have to add together our like terms as our last step of simplifying. So doing this, our final simplified answer becomes P squared plus Q squared minus 32 P q minus 34 Q plus p plus 289. And with this we have fully multiplied out our original given expression here. And so we are left 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 5 and 6. [(2m+7)-n]^2

Key Concepts

Binomial Expansion

Square of a Binomial

Combining Like Terms

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