Find each product. See Examples 5 and 6. (y+2)^3

Question

Accepted Answer

Hey everyone here we are asked for for multiplication in the given expression where we have the quantity of B plus four, cute. Now the first step here in solving this problem is to first expand our given expression. So rewriting it, it becomes the quantity of B plus four times the quantity of B plus four times the quantity of B plus four. And now we we need to start multiplying terms together. And so we can first just focus on the last two sets of parentheses and to multiply these terms together, we need to apply the foil method. So using the foil method we first take the product of the first terms in both sets of parentheses. So here we just have B times B. And then we add our now next product where we take the outside terms according to the foil method. So here we just have B times four and then adding our next product where we take the inside terms. So here we just have four times B. And then adding our last product here where we take the last terms. We just have four times four. And now we just have to simplify this expression. So from our first product we get B squared, then we have plus four B. Then we have plus another four B. And finally plus 16. And now we just have to finish up simplifying here by adding together like terms. So doing this we have B squared plus eight B plus 16. And so now with this expression that we just obtained here we can use it to replace the two sets of parentheses that we started out with. So doing this. Our original expression we had the quantity of B plus four cute. And now again using this expression we just found we can rewrite our original expression as the quantity of B plus four times the quantity of B squared plus eight B plus 16. And so now we need to continue to multiply terms together. But in this case we need to use the distributive property. So using the distributive property we first take the first term from our first set of parentheses and multiply it by our entire second set of parentheses. So here we have B times the quantity of B squared plus eight B plus 16. And now we take the second term from our first part of the expression here. So we have plus four and multiply it by the second part of our expression. So we have plus four times the quantity of B squared plus eight B plus 16. And now we just have to distribute in these terms here. So doing this our expression becomes be cute plus eight B squared plus 16, B plus four, B squared plus 32 B plus 64. And now we just have to finish simplifying here by adding together the like terms. So doing this. Our final expression becomes B cubed plus B squared plus 48 B plus 64. And with this we have fully simplified our expression and we are left with answer choice. A 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. (y+2)^3

Key Concepts

Binomial Theorem

Polynomial Expansion

Binomial Coefficients

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