Find each product. See Examples 5 and 6. (2z^4-3y)^2

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression of the quantity of 13 X. To the fourth power minus seven Y. Quantity squared. And so we want to begin solving this problem here by expanding our expression so we can clearly see what we are working with. So our expanded expression here, we have the quantity of 30 X. To the fourth power minus seven Y. Times the quantity of 13 X to the fourth power minus seven Y. And so now we can begin our multiplication process by applying the foil method. And so according to the foil method, we start by taking the product out our first terms in each set of parentheses here. So we have the quantity of 13 X to the fourth power times the quantity of 13 X to the fourth power. And then we add our next product here which will be taking the outside terms the outside terms. So we have the quantity of 13 X to the fourth power times the quantity of negative seven Y. And then again we add our next product where we take the inside terms. So we have the quantity of negative seven Y. Times the quantity of 13 X. To the fourth power. And now we can take our final product Again we add our final product here where we take the product of the last terms in each set of parentheses. So we have the the quantity of negative seven Y times the quantity of negative seven Y. So now we have finished boiling out our expression here. So we just have to start simplifying by first simplifying each of our products. So from our first product we get 169 X. To the eighth power. From our second product we get a negative term. So we have minus 91 X. To the fourth power times Y. And then our third product is the same as our second product. So we have minus 91 X. To the fourth times Y. And lastly we have a positive final product here. So we have plus 49 Y. Squared. And so now we just have to finish our simplifications here by adding together like terms. And when we get our final answer of 169 X. To the eighth power minus 182 X. To the fourth power times Y plus 49 Y. Squared. And with this we have finished multiplying our original expression here and 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. (2z^4-3y)^2

Key Concepts

Polynomial Expansion

Binomial Theorem

Combining Like Terms

Watch next