### All Algebra 1 Resources

## Example Questions

### Example Question #31 : Trinomials

Subtract the expressions below.

**Possible Answers:**

None of the other answers are correct.

**Correct answer:**

Since we are only adding and subtracting (there is no multiplication or division), we can remove the parentheses.

Regroup the expression so that like variables are together. Remember to carry positive and negative signs.

For all fractional terms, find the least common multiple in order to add and subtract the fractions.

Combine like terms and simplify.

### Example Question #1 : Simplifying Polynomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

First distribute the :

Then distribute the :

Finally combine like terms:

### Example Question #32 : Polynomials

Evaluate the following:

**Possible Answers:**

**Correct answer:**

With this problem, you need to take the trinomials out of parentheses and combine like terms. Since the two trinomials are being added together, you can remove the parentheses without needing to change any signs:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms:

### Example Question #31 : Variables

Evaluate the following:

**Possible Answers:**

**Correct answer:**

With this problem, you need to distribute the two fractions across each of the trinomials. To do this, you multiply each term inside the parentheses by the fraction outside of it:

The next step is to combine like terms, based on the variables. You have two terms with , two terms with , and two terms with no variable. Make sure to pay attention to plus and minus signs with each term when combining like terms. Since you have a positive and negative , those two terms will cancel out:

### Example Question #39 : Variables

Evaluate the following:

**Possible Answers:**

**Correct answer:**

To add these two trinomials, you will first begin by combining like terms. You have two terms with , two terms with , and two terms with no variable. For the two fractions with , you can immediately add because they have common denominators:

### Example Question #40 : Variables

Add:

**Possible Answers:**

**Correct answer:**

To add trinomials, identify and group together the like-terms: . Next, factor out what is common between the like-terms:. Finally, add what is left inside the parentheses to obtain the final answer of .

### Example Question #1 : How To Add Trinomials

Solve this system of equations for :

**Possible Answers:**

**Correct answer:**

First, we want to eliminate the variable from the set of equations. To do this, we need to make the coefficients of the two 's equal but opposite. This way, when we add the equations, we will be able to eliminate them. To make the equal but opposite to the , we need to multiply the top equation by 2 on both sides. This gives us the equation:

Then, we combine the two equations by adding them. We add the like terms together and get this equation:

Using our knowledge of algebra, we know we can divide both sides by 7 to isolate the . Doing so leaves us with our answer, .

### Example Question #42 : Variables

**Possible Answers:**

**Correct answer:**

To solve this problem, simply add the terms with like exponents and variables:

Thus, is our answer.

### Example Question #43 : Variables

Simpify into quadratic form:

**Possible Answers:**

**Correct answer:**

The first step is to combine all terms with like exponents and variables. Watch for negative signs!

Next, rearrange into standard quadratic form :

Thus, our answer is .

### Example Question #44 : Variables

Simpify into quadratic form:

**Possible Answers:**

**Correct answer:**

Let's solve this problem the long way, to see how it's done. Then we can look at a shortcut.

First, **FOIL** the binomial combinations:

FOIL stands for the multiplication between the first terms, outer terms, inner terms, and then the last terms.

Lastly, add the compatible terms in our trinomials:

So, our answer is .

**Now, let's look at a potentially faster way.**

Look at our initial problem.

Notice how can be found in both terms? Let's factor that out:

Simpify the second term:

Now, perform a much easier multiplication:

So, our answer is , and we had a much easier time getting there!

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