ACT Math : Exponents and the Distributive Property

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #71 :Exponents

For allx,\ (5x+2)^{2}=?

Possible Answers:

25x^{2}+20x+4

10x^{2}+4

25x^{2}+10x+4

25x^{2}+4

10x+4

Correct answer:

25x^{2}+20x+4

Explanation:

(5x+2)^{2}相当于(5x+2)(5x+2).

Using the FOIL method, you multiply the first number of each set5x\cdot 5x=25x^{2}, multiply the outer numbers of each set5x\cdot 2=10x, multiply the inner numbers of each set2\cdot 5x=10x, and multiply outer numbers of each set2\cdot 2=4.

Adding all these numbers together, you get25x^{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 #2 :How To Use Foil With Exponents

If, what is the value of the equation?

Possible Answers:

Correct answer:

Explanation:

Plug inforin the equation

That gives:

然后解决有限公司mputation inside the parenthesis:

答案寿ld then be

Example Question #1 :Exponents And The Distributive Property

The expression相当于__________.

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 #1 :Exponents And The Distributive Property

The expression相当于__________.

Possible Answers:

Correct answer:

Explanation:

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

Foilexpo

Example Question #3 :Exponents And The Distributive Property

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 #7 :How To Use Foil With Exponents

The rule for adding exponents is.

The rule for multiplying exponents is.

Terms with matching variablesANDexponents are additive.

Multiply:

Possible Answers:

Correct answer:

Explanation:

UsingFOILon, 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 #8 :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 #1 :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 #10 :How To Use Foil With Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

First, merely FOIL out your values. Thus:

就变成了

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

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

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