Algebra 1 : Algebra 1

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #1 : How To Add Trinomials

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

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 #4 : How To Add Trinomials

Add:

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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 #3 : How To Add Trinomials

Possible Answers:

Correct answer:

Explanation:

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

Thus,  is our answer.

Example Question #4 : How To Add Trinomials

Simpify into quadratic form: 

Possible Answers:

Correct answer:

Explanation:

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 #5 : How To Add Trinomials

Simpify into quadratic form: 

Possible Answers:

Correct answer:

Explanation:

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!

Example Question #41 : Polynomials

Add the trinomials:  

Possible Answers:

Correct answer:

Explanation:

Eliminate the parentheses and combine like-terms.

Combine all the terms.

The answer is:  

Example Question #4271 : Algebra 1

Find the sum. 

Possible Answers:

Correct answer:

Explanation:

When adding trinomials we combine together coefficients of like terms. 

Example Question #42 : Polynomials

Add the following trinomials:

Possible Answers:

Correct answer:

Explanation:

Combine like terms:

Example Question #1 : How To Subtract Trinomials

Solve this system of equations for :

Possible Answers:

Correct answer:

Explanation:

Multiply the top equation by 3 on both sides, then add the second equation to eliminate the  terms:

 

 

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