Find each product. [(3q+5)-p][(3q+5)+p]

Question

Accepted Answer

Hey everyone here we are asked to perform multiplication in the given expression where we have the quantity of the quantity of seven A plus nine minus B times the quantity of the quantity of seven A plus nine plus B. So now taking a look at our given expression, we can notice that it is actually D factored out form of the day difference of two squares. So we need to recall the difference of two squares formula which tells us that the quantity of A minus B times the quantity of A plus B is equivalent to a squared minus B squared. So with this we just need to compare our given expression with our formula here to determine our values for A. And B. While according to our formula, our value for A is just the first term from either sets of parentheses which in our case is the expression of seven A plus nine. And so now our second term must be our value for B. And so B. In our case is just going to be be. And so now that we have identified our values for A. And B, we can go ahead and substitute them into the right hand side of our differences squares formula. And find the simplified form of our original expression. So our original expression again, we had the quantity of the quantity of seven A plus nine minus B times the quantity of the quantity of seven A plus nine plus B. And so now from our difference of squares formula, we see that this expression is equivalent to the quantity of seven A plus nine squared minus B squared. And so now we just need to simplify this expression that we found. So doing this, we can first expand our first term. So we have the quantity of seven A plus nine times the quantity of seven A plus nine minus B squared. And now we just have to foil out our first two sets of parentheses here. So continuing to simplify now using the foil method we first take the product of our first terms here which we we will have seven A times seven A. And then we add our next product where we now take the outside terms. So we have the quantity of 78 times nine and then again adding our next product where we now take the inside terms. So we have nine times the quantity of seven A. And now adding our final product where we now take the last terms. So we have just nine times nine. And so now we just have this foiled out expression and then we have still the minus B squared from earlier. So we just bring that down here and now we just need to continue to simplify our expression. So from our first product we get 49 A squared from our second product we get plus 63 A. From our third product we get another plus 63 A. And from our fourth product we get plus 81 then we just bring down this minus B squared. And so now we just have to finish up our simplifications here by adding together like terms and we see our final answer. We have 49 A squared minus B squared plus 126 A plus 81. And with this we have fully multiplied out our original expression and simplified it. So 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. [(3q+5)-p][(3q+5)+p]

Key Concepts

Difference of Squares

Binomial Expressions

Polynomial Multiplication

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