When multiplying two binomials, you have to remember to multiply using the "FOIL" system (First, Outside, Inside, Last). This means you will need to multiply four different pairs of terms together to get your trinomial. 

First, you multiply the first terms in each binomial together:

Outside, you multiply the outside terms together:

Inside:

(Don't forget the negative sign!)

Last:

(Don't forget the negative sign here, either!)

Then, you add the products together:

Make sure you keep track of negative signs when doing FOIL, especially when doing the Outer and Inner steps.

When the 2 terms differ only in their sign, the -term drops out from the final product.

FOIL is a helpful way to remember how to multiply terms when we are multiplying two binomials.

F stands for first. We multiply the two "first" terms in each of the binomials.

O stands for outer. We multiply the outermost terms in the expression.

I stands for inner. We multiply the innermost terms in the expression.

L stands for last. We multiply the two "last" terms in each of the binomials.

F - 

O - 

I - 

L - 

Now we combine each part using addition to get:

The two terms in the middle can be combined to get our final answer:

Recall that using FOIL means multiplying the first terms, then the outside terms, next the inside terms, and finally, the last terms. Therefore, after multiplying all of those, you should get: . Combine your like terms to get a final answer of: .

Recall that FOIL means multiplying the first terms, then outside terms, next inside terms, and then the last terms. Therefore, when you do those steps, you get: . Simplify the middle terms to get your answer of .

To solve this problem, recall that you will be using the FOIL method to mutlply these binomials: . Then, combine like terms to get your answer: .

To multiply these binomials, use the FOIL method: . Combine like terms to get your answer of .

This function can be expanded as

where

x=number of $0.05 changes to the initial price which will maximize potential revenue.

Since we are seeking to maximize  profit, we need to find the point in this function, where a given number, x, of changes to the original price yields the greatest additional profit by balancing the additional revenue per cookie with the $0.05 decrease in cost.

In other words, we are seeking the vertex of this parabola.

First we convert the profit function into quadratic form by FOILing:

rearranging this, we find that:

Recall that

So, in order to maximize profits, we should reduce each cookie's cost by $.05 5 times.

We should sell each cookie for $0.75

To FOIL (First, Outer, Inner, Last), we start be multiplying the first terms together:

Then the Outer terms:

Then the Inner terms:

And finally the Last terms:

We then collect each of the answers and put them in descending order of degree of their exponent: