Find each product. See Examples 5 and 6. (4m+2n)^2

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression of the quantity of four X plus nine Y squared. Now our first step here in solving this problem is to expand our expression so we can clearly see what we are multiplying together. So expanding our expression, we have the quantity of four X plus nine Y times the quantity of four X plus nine Y. So now we can start multiplying our terms together using this expanded expression using the foil method. So with the foil method, it tells us to begin by taking the product of the first terms in each set of. So here we'll start by having the quantity of four X times the quantity of four X. And then we need to add our next product which according to the foil method, we take the product of the outside terms here. So we have the quantity of four X times the quantity of nine Y. And then adding our third product, we take the product of the inside terms. So we have the quantity of nine y times the quantity of four X. And now we take our final product here, again adding the product of the last terms. So we have the quantity of nine Y times the quantity of nine Y. So now we have fully foiled out our expression here. So we just have to start simplifying our products. So from our first product we get 16 X squared. And then we have plus our second prod here which was 36 X. Y. And our third product is the same as the second product. So we have plus another 36 X. Y. And from our final product we have plus 81 Y squared. So now our last step here is to just finish up simplifying by adding together like terms. So we see our final answer here. We have 16 X squared plus X. Y plus 81 Y squared. And with this we have finished fully multiplying our original expression and 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. (4m+2n)^2

Key Concepts

Binomial Expansion

Squaring a Binomial

Combining Like Terms

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