### All Algebra 1 Resources

## Example Questions

### Example Question #32 : Quadratic Equations

What is the equation that has the following solutions?

**Possible Answers:**

**Correct answer:**

This is a FOIL-ing problem. First, set up the numbers in a form we can use to create the function.

Take the opposite sign of each of the numbers and place them in this format.

Multiply the in the first parentheses by the and 8 in the second parentheses respectively to get

Multiply the in the first parentheses by the and 8 in the second parentheses as well to give us .

Then add them together to get

Combine like terms to find the answer which is **.**

### Example Question #1 : Distributive Property

Simplify the following expression.

**Possible Answers:**

**Correct answer:**

Simplify using FOIL method.

Remember that multiplying variables means adding their exponents.

F:

O:

I:

L:

Combine the terms. Note that we cannot simplify further, as the exponents do not match and cannot be combined.

### Example Question #2 : Distributive Property

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Distributive Property

What are the factors of ?

**Possible Answers:**

**Correct answer:**

To find the factors, you must determine which of the sets of factors result in the polynomial when multiplied together. Using the FOIL method, a set of factors with the form will result in . Applying this format to the given equation of , must equal 11 and must equal 24. The only set that works is .

### Example Question #4 : Distributive Property

Expand:

**Possible Answers:**

**Correct answer:**

If you use the FOIL method, you will multiply each expression individually. So, becomes , which simplifies to .

### Example Question #5 : Distributive Property

Simplify the expression below.

**Possible Answers:**

**Correct answer:**

Use the distributive property to simplify the expression. In general, .

Now we can begin to combine like terms through multiplication.

We cannot simplify further.

### Example Question #34 : Quadratic Equations

Multiply the binomials below.

**Possible Answers:**

**Correct answer:**

The FOIL method yields the products below.

First:

Outside:

Inside:

Last:

Add these four terms, and combine like terms, to obtain the product of the binomials.

### Example Question #35 : Quadratic Equations

Factor the expression below.

**Possible Answers:**

**Correct answer:**

First, factor out an , since it is present in all terms.

We need two factors that multiply to and add to .

and

Our factors are and .

We can check our answer using FOIL to get back to the original expression.

First:

Outside:

Inside:

Last:

Add together and combine like terms.

Distribute the that was factored out first.

### Example Question #6 : Distributive Property

**Possible Answers:**

**Correct answer:**

### Example Question #7 : Distributive Property

Expand:

**Possible Answers:**

**Correct answer:**

To expand , use the FOIL method, where you multiply each expression individually and take their sum. This will give you

or

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