Exponents and the Distributive Property

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ACT Math › Exponents and the Distributive Property

Questions 1 - 10
1

Distribute and simplify:

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

Lastly, combine any terms that allow this (usually, but not always, the two middle terms).

Arrange your answer in descending exponential form, and you're done.

2

Distribute and simplify:

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

Lastly, combine any terms that allow this (usually, but not always, the two middle terms).

Arrange your answer in descending exponential form, and you're done.

3

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,

4

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,

5

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.

6

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.

7

Distribute and simplify:

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

Lastly, combine any terms that allow this (usually, but not always, the two middle terms). In this case, no two terms are compatible.

Arrange your answer in descending exponential form, and you're done.

8

Distribute and simplify:

Explanation

To FOIL this binomial distribution, we simply distribute the terms in a specific order:

Multiply the First terms:

Multiply the Outer terms:

Multiply the Inner terms:

Multiply the Last terms:

Lastly, combine any terms that allow this (usually, but not always, the two middle terms). In this case, no two terms are compatible.

Arrange your answer in descending exponential form, and you're done.

9

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

10

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

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