This is a classic FOIL problem. FOIL stands for first, outer, inner, and last. It describes a process of multiplying together polynomials. Essentially, you are multiplying every combination of terms from the first set of parentheses and the second set of parentheses. You start with the first two terms, then the outer two terms, then the inner two terms, and finally the last two terms.

For , your first two terms are  and , and . Your outer two terms are  and , and . Your inner two terms are  and , and . Your last two terms are  and , and .

Ultimately, once you combine and add everything together, you get

.

You finish by combining like terms. The two like terms here are  and  and . 

Therefore, your final answer is

.

To foil these two equations, we'll need to multiply them together. To multiply them together, you'll have to take each term from the first equation and multiply them individually with each term in the second equation.

We'll start with  from the first equation.

Multiply  from the first equation with  from the second equation.

Multiply  from the first equation with  from the second equation.

Now we'll use the  from the first equation.

Multiply the  from the first equation with the  from the second equation.

Multiply the  from the first equation with  from the second equation.

We won't do this method with the second equation as that will only give us the same answer. Now take all of your answers and string them together, like so:

We can combine our  and  because they are under the same power of ; which is one.

Since we cannot combine anymore like terms, we can take what we have left and put it as our final equation.

Your answer is 

In order to foil these two equations, we're going to have to multiply them together. In order to do that, you're going to have to take each term from the first equation and separately multiply them with all the terms in the second equation.

First we'll start with  from the first equation.

Multiply  from the first equation with the  from the second equation:

Multiply  from the first equation with the  from the second equation:

Now we'll work with the .

Multiply the  from the first equation with the  from the second equation:

Multiply the  from the first equation with the  from the second equation:

We won't do this again with the second equation as that will just give us the same answers. Now take all the answers and string them together into an equation like so:

The  and  can be combined together as they share the same power, which is one.

Since there is nothing left to combine, we can leave the equation as is.

Your answer should be 

Foiling means to take two equations and merge them into one. It's also the same as saying you want to multiply one equation with another, which is what we'll be doing.

Our two equations are  and , which is the same as . In order to multiply these two equations together, you must first multiply the first unit  in your equation with everything in the second equation, then the second unit  with everything in your second equation.

Multiply the  in the first equation with the  from the second equation:

Multiply the  in the first equation with the  from the second equation:

Now multiply the  with the  from the second equation:

Multiply the  from the first equation with the  from the second equation:

We won't multiply the second equation with the first one like we did above, as that would give us the same answers. Take all the answers you got from above and now string them together like so:

We're almost done, but we seem to be have more than one ;  and . These two terms can be combined like so: 

Since nothing else seems to have more than one of itself, we can now put the equation together. Make sure to go in order of highest power of  to the lowest power of .

Your answer is 

The FOIL technique is used to multiply or expand two binomials. None of the other expressions represent two binomials. The closest representation would be . This expression calls for the multiplication of a binomial and a monomial, so a more straightforward application of the distributive property would work in that case.

One can use the FOIL method.

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Adding them up, we get the polynomial , in the customary form of a polynomial.

So FOIL works in this case

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This a case to FOIL

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Even though there is an  in one of the expressions, the expression is STILL a binomial, and should be treated as such. FOIL is used with the multiplication of two binomials, so FOIL works here.

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Add the terms: 

The FOIL method works because there are two binomials.

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Adding gives the polynomial