How to subtract trinomials - Algebra 1

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:

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: .

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 .

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!

Now we add/subtract all like terms, yielding:

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:

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.)

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.)

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.

When subtracting trinomials we distribute the negative sign and turn it into addition.

We then combine together coefficients of like terms.