Find each product. See Examples 3–5. (3y-5)(3y+5)(9y^2-25)

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of seven a minus six times the quantity of seven A plus six times the quantity of 49 A squared minus 36. Now our first step here before we begin multiplying, we want to start by reducing this expression and we can do this by first noticing our first two sets of parentheses here and that they are a factored out form of our difference of squares formula. So we need to recall the difference of squares formula which tells us that the quantity of a minus B times the quantity of A plus B is equal to a squared minus B squared. So now we just have to compare our formula with the first two sets of parentheses from our original expression to determine our values for A and B. So looking at our formula, we see that the first term is going to be A. So A. In our case for our expression is going to be seven A. And then the next term is just our B values. So B is just going to be six. So now we can go ahead and use these identified values for A and B. And substitute them into the right hand side of our formula. So we see that the original expression, the first two sets of parentheses, we had the quantity of seven a minus six times the quantity of seven A plus six. And from our difference of squares formula, we see that this expression is the equivalent to the quantity of seven a squared minus six squared. And now just simplify this expression here we see that we have the different of two squares of 49 A squared minus 36. So now we can go ahead and substitute this expression here into our original expression. So originally we had again the quantity of seven a minus six times the quantity of seven A plus six times the quantity of 49 A squared minus 36. And now substituting in our expression we found earlier for our first two sets of parentheses, we can rewrite our expression as the quantity of 49 A squared minus 36 times the quantity of 49 A squared minus 36. So now from here we just have to apply the foil method to start the multiplication process. So doing the foil method, we begin again the foil method. We begin with the first terms. So we begin with the quantity of 49 A squared times the quantity of 49 A squared. And next we can move on to our next terms here. So we add the outside the product of the outside terms which are 49 A squared times negative 36. And next we move to the inside terms. So adding the product of the inside terms, we have negative 36 times 49 A squared. And lastly We just move on to the last terms the last terms in both sets of parentheses. So we have negative 36 times negative 36. And now we just have to start simplifying our expression here. So our first product we get 2401 A. To the fourth power. Then from our second product we get A squared. From our next product we get again negative or sorry we get minus 1764 A. Squared. And then from our last product we get positive plus 1296. And now just simplifying adding together liked terms we see that our final answer here is 2401 A. To the fourth power minus 30 sorry 3528 A squared plus 1296. And with this we have fully multiplied our given expression out. And so 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 3–5. (3y-5)(3y+5)(9y^2-25)

Key Concepts

Factoring and Products of Binomials

Difference of Squares

Multiplying Polynomials

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