Find each product. See Examples 5 and 6. (z-3)^3

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of a minus seven. Cute! Now our first step here is to just expand our given expression. So we will have the quantity of a minus seven times the quantity of a minus seven times the quantity of a minus seven. And so now we can start multiplying terms together by applying the foil method. Well we can focus on just the last two sets of parentheses for now and doing this applying the foil method, we take the first terms from both sets of parentheses. So we just have a times A. And then we add our next product here which again according to the foil method, we now take the outside terms. So we just have a times the quantity of negative seven and then again adding our next product where in this case we take the inside terms. So we have the quantity of negative seven times A. And then we again add our now final product here where we take the last terms from both sets of parentheses. So we have the quantity of negative seven times the quantity of negative seven. And so now we just have to start simplifying this expression. So from our first product we get a squared and then we have minus seven A. And then we have again another minus seven A. And lastly we have plus 49 And now we just have to finish simplifying by adding together our like terms. So we have the expression of a squared -14 a plus 49. And with this expression we can now substitute it into our original expression to replace the two sets of parentheses. We grouped together from earlier. So doing this our original expression again we had the quantity of a minus seven cubed and now rewriting it using the expression we found we now have the quantity of a minus seven times the quantity of a squared minus 14 A plus 49. And now from here we need to continue to multiply terms together. But now we will use the distributive property. So for the distributive property we take both terms individually and multiply them by the entire second set of parentheses. So doing this again, taking the terms from our first set of parentheses, we have a times the quantity of a squared minus 14 A plus 49. And then we have minus seven times the quantity of a squared minus 14 A plus 49. And now we just have to distribute it dish tribute in out these terms on the outside of our parentheses here. So doing this we have a cubed minus 14 A squared plus 49 a minus seven A squared plus a minus 343. And now our last step here is to just combine our like terms. So our final simplified expression becomes a cubed minus 21 A squared plus 147 a minus 343. And with this we have found our final simplified answer here, so we are left with answer choice. C. 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. (z-3)^3

Key Concepts

Binomial Expansion

Cubic Functions

Factoring and Roots

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