# ACT Math : How to use FOIL with exponents

## Example Questions

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### Example Question #1 : How To Use Foil With Exponents

For all  ?

Explanation:

is equivalent to .

Using the FOIL method, you multiply the first number of each set , multiply the outer numbers of each set , multiply the inner numbers of each set , and multiply outer numbers of each set .

Adding all these numbers together, you get

### Example Question #2 : How To Use Foil With Exponents

Explanation:

FOIL the first two terms:

Next, multiply this expression by the last term:

Finally, combine the terms:

### Example Question #1 : Exponents And The Distributive Property

If , what is the value of the equation ?

Explanation:

Plug in  for  in the equation

That gives:

Then solve the computation inside the parenthesis:

### Example Question #3 : Exponents And The Distributive Property

The expression  is equivalent to __________.

Explanation:

Use FOIL and be mindful of exponent rules. Remember that when you multiply two terms with the same bases but different exponents, you will need to add the exponents together.

### Example Question #2 : Exponents And The Distributive Property

The expression  is equivalent to __________.

Explanation:

Remember to add exponents when two terms with like bases are being multiplied.

### Example Question #5 : How To Use Foil With Exponents

Use the FOIL method to simplify the following expression:

Explanation:

Use the FOIL method to simplify the following expression:

Step 1: Expand the expression.

Step 2: FOIL

First:

Outside:

Inside:

Last:

Step 2: Sum the products.

### Example Question #6 : Exponents And The Distributive Property

The rule for adding exponents is .

The rule for multiplying exponents is .

Terms with matching variables AND exponents are additive.

Multiply:

Explanation:

Using FOIL on , we see that:

First:

Outer:

Inner:

Last:

Note that the middle terms are not additive: while they share common variables, they do not share matching exponents.

Thus, we have . The arrangement goes by highest leading exponent, and alphabetically in the case of the last two terms.

### Example Question #5 : Exponents And The Distributive Property

The concept of FOIL can be applied to both an exponential expression and to an exponential modifier on an existing expression.

For all  = __________.

Explanation:

Using FOIL, we see that

First =

Outer =

Inner =

Last =

Remember that terms with like exponents are additive, so we can combine our middle terms:

Now order the expression from the highest exponent down:

Thus,

### Example Question #1163 : Algebra

Square the binomial.

Explanation:

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

### Example Question #8 : Exponents And The Distributive Property

Simplify:

Explanation:

First, merely FOIL out your values.  Thus:

becomes

Now, just remember that when you multiply similar bases, you add the exponents.  Thus, simplify to:

Since nothing can be combined, this is the final answer.

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