Find each product. See Examples 5 and 6. (q-2)^4

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of x minus six raised to the fourth power. Now our first step here before we start multiplying any terms together, we just want to expand our given expression. So doing this expanding, we have the quantity of x minus six times the quantity of X minus six times the quantity of X minus six and times equal E. of X -6. So now that we have our given expression fully expanded, we can go ahead and apply the foil method so that we can start multiplying some terms together. Now when we apply the foil method we're just going to focus on the first two sets of parentheses for right now. So doing this again using the foil method, we first take the product of the first terms in each set of parentheses. So here we just have X times X. And then we add the next product which according to the foil method is now we take the outside terms. So we have X times the quantity of negative six. And then again we add our next product where we take the product of the inside terms. So we have the quantity of negative 6, 10 times the quantity of X. And now for our final product we just take the last terms here. And so we have the quantity of negative six times the quantity of negative six. So now our next step since we finished boiling out our first part of our expression we just have to start simplifying. So we see from our first product that we have X squared. And then from our second product we get minus six X. Our third product is the same as our second product. So we have another minus six X. And then from our fourth product we get plus 36. So now we just have to finish up simplifying here by adding together like terms. And we see that our multiplied expression becomes an X squared minus 12 X plus 36. So now again this expression here, these terms that we obtained were for the first two sets of parentheses. But since our last two sets of parentheses are also the same, we'll just apply what we found for both portions of our expression. So again we had the quantity of x minus six times the quantity of x minus six times the quantity of x minus six times the quantity of x minus six. And now using the expression we got from foiling out our first two sets of parentheses, we can rewrite our given expression as the quantity of X squared minus 12 X plus 36 times the quantity of X squared minus 12 X plus 36. So now the next step here is to apply the distributive property where we're going to take each term from the first set of parentheses and multiply it by the entire second set of parentheses. So doing this, we just need to rewrite our expression here according to the distributive property. So we're going to have our first term here which is X squared times the quantity of X squared minus X plus 36. And then we take our next term. We first add the next product where we take the next term which is negative 12 X. And then we multiply this by the quantity of X squared minus 12 X plus 36. And lastly we add the last product where we take the last term. So we have plus 36 times the quantity of X squared minus 12 X plus 36. And now we just have to start simplifying by distributing in these outside terms into our expressions here. So doing this we have X to the fourth power minus X cubed plus 36 X squared minus 12 X cubed plus X squared minus 432 X plus plus 36 X squared minus 432 X plus 1296. And now our last step here is to just combine our like terms in this expression. Just to simplify our expression and we get the final answer of X to the fourth Power minus 24 X cute plus 216 X squared minus 864 X plus 1296. And with this we have fully multiplied out our given expression here and we have simplified our expression 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. (q-2)^4

Key Concepts

Polynomial Expansion

Binomial Theorem

Coefficients and Combinations

Watch next