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:

To FOIL (First, Outer, Inner, Last), we start by multiplying the first term in each grouping together:

Then we multiply the outer terms together (the first term in the first grouping, the last term in the second grouping):

Then we multiply the inner terms together (the second term in the first grouping, the first term in the second grouping):

And finally the last term in each grouping:

We can then collect everything back into our function:

And combine like terms (in this case, both terms with an  in them):

This problem uses the distributive property. When using the distributive property on two sums, we apply the FOIL method. FOIL is an acronym that means, First, Outer, Inner, Last. This means we multiply the first term by the first term, the outer term by the outer term, the inner term by the inner term, and the last term by the last term. Take all of these products and add them together. To put this in a more general equation:

Applying this formula to our problem we have,

And thus, our answer is

Recall that FOIL means multiplying the first terms, then outside terms, next inside terms, and finally, the last terms:

.

Then, combine like terms to get your answer of

.

Use the FOIL method to expand the binomials.

Simplify the terms on the right side of the equal sign.

Combine like-terms.

The answer is:  

Use FOIL to multiply these binomials.

First multiply the first terms

,

then the outside terms

,

next the inside terms

,

and finally, the last terms

.

That gives you

.

Combine like terms to get your final answer of

.

Remember to use FOIL when multiplying.

Multiply the first terms

,

then the outside terms

,

next the inside terms

,

and finally, the last terms

.

Put those all together to get your answer:

Distribute the first term of the binomial with both terms of the second binomial.

Distribute the second term of the binomial with both terms of the second binomial.

Add the terms together.

The answer is:  

To multiply these two binomials, use FOIL.

Multiply the first terms

,

then the outside terms

,

next the inside terms

,

and finally the last terms

.

Put those all together to get:

.

Combine like terms to get your final answer of