Algebra 1 : How to subtract trinomials

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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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:

 

 

Example Question #2 : How To Subtract Trinomials

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

To subtract these two trinomials, you first need to flip the sign on every term in the second trinomial, since it is being subtrated:

Next you can combine like terms. You have two terms with , two terms with , and two terms with no variable:

Example Question #1 : How To Subtract Trinomials

Subtract:

Possible Answers:

Correct answer:

Explanation:

When subtracting trinomials, first distribute the negative sign to the expression being subtracted, and then remove the parentheses: 

Next, identify and group the like terms in order to combine them: .

Example Question #51 : Variables

Simpify into quadratic form: 

Possible Answers:

Correct answer:

Explanation:

First, FOIL the binomial combinations:

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

Next, distribute  into our new binomial and combine all compatible terms:

So, our answer is .

Example Question #52 : Variables

Simplify the following expression: 

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 #3 : How To Subtract Trinomials

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

 

Now we add/subtract all like terms, yielding:

Example Question #4 : How To Subtract Trinomials

Subtract  with .

Possible Answers:

Correct answer:

Explanation:

Group both trinomials with a parenthesis and set up the expression.

Simplify by removing the parentheses, distribute the negative sign, and rewrite the expression.

Combine like-terms.

The answer is:  

Example Question #3 : How To Subtract Trinomials

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To subtract polynomials, simply combine like terms. But be extremely careful to distribute the negative to ALL terms in the second polynomial! (Consider subtracting vertically to help.)

Example Question #4 : How To Subtract Trinomials

Possible Answers:

Correct answer:

Explanation:

To subtract polynomials, simply combine like terms. But be extremely careful to distribute the negative to ALL terms in the second polynomial! (Consider subtracting vertically to help.)

Example Question #1 : How To Subtract Trinomials

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To subtract polynomials, simply combine like terms. But be extremely careful to distribute the negative to ALL terms in the second polynomial! (Consider subtracting vertically to help.)

Here, notice that the terms are not in the same order in both polynomials.

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