Find each product. See Examples 5 and 6. [(3a+b)-1]^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 14 X plus y minus a squared. Now our first step here is to just expand our given expression. So doing this we have the quantity of the quantity of 14 X plus y minus eight time times the quantity of the quantity of 14 X plus Y minus eight. And so now that we have fully expanded our original expression we can now apply the foil method and start multiplying our terms together. So recalling the foil method, we first take the product of our first terms and both sets of parentheses. So we have the quantity of 14 X plus Y times the quantity of 14 X plus Y. And now we add our next product which again according to the foil method, we now take the outside terms. So we have the quantity of 14 X plus Y times the quantity of negative eight. Again adding our next product. We now take the inside terms. So we have the quantity of negative eight times the quantity of X plus Y. And now adding our last product here where we take the last terms from both sets of parentheses, we have the quantity of negative eight times the quantity of negative eight. And so now from here we just need to start simplifying So beginning with our first product here we see that we actually have to foil out these terms again. So doing this, we first have 14 X times 14 X. And then we have plus 14 X Times Y plus Y. Times 14 X plus Y. Times Y. And then from our next product we just have to distribute this negative eight term. So we have minus eight times the quantity of X. Then we have minus eight times Y. And from our third product here we actually have the same product where we distribute the negative eight term. So doing this we have minus eight times the quantity of 14 X minus eight times Y. And then adding our last product here where we had negative eight times negative eight. Well that is just equivalent to plus 64. And so now we just need to continue to simplify here and we see from our first product our 14 X. Quantity squared we get 196 X squared. And then we have plus 14 X. Y. And we have another plus 14 X. Y. And then we have plus Y squared. And then from our next product here we have minus 112 X minus eight Y. Then we have another minus 112 X minus eight Y. And lastly we just have plus 64. So now our last simplification here that we have to make is to combine the like terms. So doing this, our final expression becomes X squared plus Y squared plus 28 X Y minus X minus 16 Y plus 64. And with this we have fully multiplied out our original expression here and so we are left 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. [(3a+b)-1]^2

Key Concepts

Binomial Expansion

Algebraic Manipulation

Exponent Rules

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