Find each product. See Examples 5 and 6. (r+3)^4

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of P plus five raised to the fourth power. Now our first step here is to just expand our given expression. So we will have the quantity of P plus five times the quantity of P plus five times the quantity of P plus five times the quantity of P plus five. And so now we need to apply the foil method so we can start multiplying our terms together. Now here we will focus on just the first two sets of parentheses for now. So again foiling out these two parentheses here we begin with the first terms from both sets. So we have P times P. And now we add our next product where according to the foil method we take the outside terms. So we just have P times five and then again adding our next product where we now take the inside terms. So we have five times P. And adding our last product. Where we take the last terms. We just have five times five. And now we just need to simplify this expression here and we see we have P squared we have P squared plus five P plus another five P plus 25. And now adding together like terms. We see we have the expression of we have the expression of P squared plus 10 P plus 25. And now looking at this expression we obtained we see we can use it to replace our first two sets of parentheses and we can also use it to replace our last two sets of parentheses. Since both parts of the expression are equivalent. So doing this we can rewrite our original expression. So we had the quantity of P plus five raised to the fourth power. And now using this expression that we obtained earlier we can rewrite our original expression as the quantity of P squared plus 10 p plus 25 times the quantity of P squared plus 10 P plus 25. So now we just need to continue to multiply out our terms. But in this case we are going to apply the distributive property where we will take each of the terms in the first set of parentheses and multiply it by the entire second set of parentheses. So what I mean by this we start with our first term here which is p squared and we multiply it by the quantity of p squared plus 10 P plus 25. And then for our next term we have plus 10 p times the quantity of p squared plus 10 P plus 25. And then for our last term we have plus 25 times the quantity of P squared plus 10 P plus 25. And now we just need to distribute each of these terms into the respective set of parentheses here. So doing this we get the multiplied expression of P to the fourth power plus 10 p. Cute plus 25 p squared plus 10 p cubed plus 100 p squared plus 250 p plus 25 P. Squared plus 250 p plus 625. And now our last appears to just combine our like terms. So we see a our final simplified expression becomes P. To the fourth power plus 20 P cubed plus 150 P. Squared plus 500 P plus 625. And with this we have found our simplified expression for the full multiplied out expression of our original expression and therefore 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. (r+3)^4

Key Concepts

Binomial Theorem

Binomial Coefficients

Polynomial Expansion

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