### All ACT Math Resources

## Example Questions

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

For all ?

**Possible Answers:**

**Correct answer:**

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 #1 : Exponents And The Distributive Property

**Possible Answers:**

**Correct answer:**

FOIL the first two terms:

Next, multiply this expression by the last term:

Finally, combine the terms:

** **

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

If , what is the value of the equation ?

**Possible Answers:**

**Correct answer:**

Plug in for in the equation

That gives:

Then solve the computation inside the parenthesis:

The answer should then be

### Example Question #4 : How To Use Foil With Exponents

The expression is equivalent to __________.

**Possible Answers:**

**Correct answer:**

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 #5 : How To Use Foil With Exponents

The expression is equivalent to __________.

**Possible Answers:**

**Correct answer:**

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

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

Use the FOIL method to simplify the following expression:

**Possible Answers:**

**Correct answer:**

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 #1 : 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:

**Possible Answers:**

**Correct answer:**

Using **FOIL **on , we see that:

**F**irst:

**O**uter:

**I**nner:

**L**ast:

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 #2 : 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 *, * = __________.

**Possible Answers:**

**Correct answer:**

Using FOIL, we see that

**F**irst =

**O**uter =

**I**nner =

**L**ast =

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 #1 : Exponents And The Distributive Property

Square the binomial.

**Possible Answers:**

**Correct answer:**

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

### Example Question #10 : How To Use Foil With Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

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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