ACT Math : How to use FOIL with exponents

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Use Foil With Exponents

For all x,\ (5x+2)^{2}= ?

Possible Answers:

25x^{2}+20x+4

10x+4

25x^{2}+4

10x^{2}+4

25x^{2}+10x+4

Correct answer:

25x^{2}+20x+4

Explanation:

(5x+2)^{2} is equivalent to (5x+2)(5x+2).

Using the FOIL method, you multiply the first number of each set 5x\cdot 5x=25x^{2}, multiply the outer numbers of each set 5x\cdot 2=10x, multiply the inner numbers of each set 2\cdot 5x=10x, and multiply outer numbers of each set 2\cdot 2=4.

Adding all these numbers together, you get 25x^{2}+10x+10x+4=25x^{2}+20x+4

Example Question #1 : How To Use Foil With Exponents

 

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

Plug in  for  in the equation

That gives:

Then solve the computation inside the parenthesis:

The answer should then be 

 

 

Example Question #3 : How To Use Foil With Exponents

The expression  is equivalent to __________.

Possible Answers:

Correct answer:

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.

Foilexpo

 

Example Question #2 : How To Use Foil With Exponents

The expression  is equivalent to __________.

Possible Answers:

Correct answer:

Explanation:

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

 

Foilexpo

Example Question #5 : How To Use Foil With Exponents

Use the FOIL method to simplify the following expression:

Possible Answers:

Correct answer:

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 #3 : 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: 

Possible Answers:

Correct answer:

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 #1 : 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  = __________.

Possible Answers:

Correct answer:

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 #3 : How To Use Foil With Exponents

Square the binomial.

Possible Answers:

Correct answer:

Explanation:

We will need to FOIL.

First:

Inside:

Outside:

Last:

Sum all of the terms and simplify.

Example Question #4 : How To Use Foil With Exponents

Simplify:

Possible Answers:

Correct answer:

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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