Find each product. See Examples 5 and 6. (5r-3t^2)^2

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression of the quantity of 11 x minus 15 Y squared, all squared. So now we want to begin before we start multiplying, we want to begin by expanding our expression here so we can clearly see what we are working with. So our expanded expression, we have the quantity of 11 x minus 15 Y squared times the quantity of 11 X minus 15 Y squared. And now to start multiplying here, we want to apply the foil method. So the foil method tells us to start with the first terms in each set of parentheses and take the product of the first term. So we have the quantity of 11 X times the quantity of 11 X. And now we add the product of our next terms. Which according to the foil method, we take the outside terms. So here we have the quantity of 11 X times the quantity of negative 15 Y squared. And now again we add the next product where we will take the product of our inside terms and our inside terms here we have the quantity of negative 15 Y squared times the quantity of 11 X. And for our last product again we add the last product and we are taking the last terms here. So we have the quantity of negative 15 Y squared times the quantity of negative 15 Y squared. So now that we have foiled out our original expression, we just have to start simplifying our products here. So beginning with our first product we get 121 X. Squared. And then for our next product we get a negative so we have minus 165 X. Y. Squared. And then our third product is the same. So we have another minus 165 X. Y squared. And for our last product we have plus 225 Y. To the fourth power. And so now we just have to finish our simplifications here by adding together like terms. And we see that our final answer here is 121 X squared minus 330 X. Y squared plus 225 Y to the fourth power. And with this we have fully finished our multiplication of our original expression here. And so we are left with answer choice B. 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. (5r-3t^2)^2

Key Concepts

Binomial Expansion

Squaring a Binomial

Combining Like Terms

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