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 #1 : 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 #2 : How To Use Foil With Exponents

If , what is the value of the equation ?

Explanation:

Plug in  for  in the equation

That gives:

Then solve the computation inside the parenthesis:

The answer should then be

Example Question #1 : How To Use Foil With Exponents

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 : How To Use Foil With Exponents

The expression  is equivalent to __________.

Explanation:

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

Example Question #3 : 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 #2 : How To Use Foil With Exponents

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 #6 : How To Use Foil With Exponents

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 #4 : Exponents And The Distributive Property

Square the binomial.

Explanation:

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

Example Question #8 : How To Use Foil With Exponents

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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