### All ACT Math Resources

## Example Questions

### Example Question #3 : Simplifying

Simplify the following binomial:

**Possible Answers:**

**Correct answer:**

The equation that is presented is:

To get the correct answer, you first need to combine all of the like terms. So, you can subtract the from the , leaving you with:

From there, you can reduce the numbers by their greatest common denominator, in this case, :

Then you have arrived at your final answer.

### Example Question #4 : Simplifying

Simplify the following binomial expression:

**Possible Answers:**

**Correct answer:**

First, combine all of the like terms that you are able:

Then, reduce by the greatest common denominator (in this case, ):

### Example Question #5 : Simplifying

Simplify the following binomial:

**Possible Answers:**

**Correct answer:**

The equation presented in the problem is:

First you have to combine the like terms, i.e. combining all instances of and :

Then, you can factor out the common to get your answer

### Example Question #1 : How To Multiply Binomials With The Distributive Property

Which of the following expressions is equivalent to: 6x (m^{2 }+yx^{2 }*–*3)?

**Possible Answers:**

6xm^{2} + 7x^{3} -18

xm^{2} + 7x^{3} -18

6xm^{2} + 6yx^{2} -18x

6xm^{2} + 6yx^{3} -18x

6xm^{2} + 6yx^{3} -18

**Correct answer:**

6xm^{2} + 6yx^{3} -18x

6x (m^{2 }+yx^{2 }*–*3)= 6x∙m^{2 }+ 6xyx^{2} – 6x∙3= 6xm^{2} + 6yx^{3 }-18x (Use Distributive Property)

### Example Question #2 : How To Multiply Binomials With The Distributive Property

Which of the following expressions is equivalent to: ?

**Possible Answers:**

**Correct answer:**

Use the distributive property to multiply by all of the terms in :

### Example Question #3 : How To Multiply Binomials With The Distributive Property

If and are constants and is equivalent to , what is the value of ?

**Possible Answers:**

Cannot be determined from the given information.

**Correct answer:**

The question gives us a quadratic expression and its factored form. From this, we know

At this point, solve for t.

Now, we can plug in to get

.

Now, use FOIL to get s.

### Example Question #4 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #5 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #6 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**

In this problem, we are to multiply the two binomials using the FOIL method. This method stands for the order in which you multiply the variables. F stands for the first term of each binomial. O stands for the outside terms, meaning the first term of the first binomial and the last term of the second. I stands for the inside terms, meaning the second term of the first binomial and the first term of the second. L stands for the last term of each binomial. Once you do this, you simply add each part together to recieve your polynomial answer. Here is how our problem is solved:

### Example Question #7 : How To Multiply Binomials With The Distributive Property

Which expression is equal to ?

**Possible Answers:**

**Correct answer:**