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Add & Subtract Polynomials

In this video, learn how to add & subtract polynomials by combining like terms.

In this video, we are going to look at adding and subtracting polynomials.
For example:
To simplify the expression:
(3x^2+5x+3xy)+(4x^2-3x+7xy)
combine the like terms to get the final answer of
7x^2+2x+10xy
To simplify the expression:
(3x^2+5x+3xy)-(4x^2-3x+7xy)
we can either keep-change-change or distribute the negative to get
(3x^2+5x+3xy)+(-4x^2+3x-7xy)
Then, combine like terms to get the final answer of
-x^2+8x-4xy
Sometimes, every term may not line up, such as in the expression
(4x^2+5x)-(3x^2+2x-4y)
Solve as you would normally by either keep-change-change or distributing the negative, and then combining like terms to get a final answer of
x^2+3x+4y

Video-Lesson Transcript

Now, let’s discuss how to add and subtract polynomials.

For example, we have

3x^2 + 5x + 3xy
+ 4x^2 - 3x + 7xy

It’s helpful to align the like terms so its easier to combine them.

Now, we combine the like terms

7x^2 + 2x + 10xy

Or we can write the two polynomials on a straight line like this:

3x^2 + 5x + 3xy + (4x^2 - 3x + 7xy)

Now, we distribute the + sign.

It’s like we have +1 at the beginning of the polynomial inside the parenthesis.

So we’ll have

3x^2 + 5x + 3xy + 4x^2 - 3x + 7xy

Then, look for the like terms and combine them.

7x^2 + 2x + 10xy

We got the same answer as the first.

Add & Subtract Polynomials

Let’s look at an example which involves subtraction.

3x^2 + 5x + 3xy
- 4x^2 - 3x + 7xy

Since we’re subtracting polynomials, we should do keep-change-change.

Let’s keep the top the same.

3x^2 + 5x + 3xy

Then change the overall minus sign into addition.

Lastly, we change the signs of each term.

-4x^2 + 3x - 7xy

Now, it’s time for us to combine the like terms

3x^2 + 5x + 3xy
+ (-4x^2) + 3x - 7xy

And the answer is

-x^2 + 8x - 4xy

Now, let’s do this on a straight line.

3x^2 + 5x + 3xy - (4x^2 - 3x + 7xy)

Let’s distribute the negative sign into the polynomial in the parenthesis. Just like there’s a -1 at the beginning.

So, we’ll have

3x^2 + 5x + 3xy - 4x^2 + 3x - 7xy

Then, combine the like terms. We now have

-x^2 + 8x - 4xy

Same as the first answer.

Let’s look at a pretty difficult problem here

(4x^2 + 5x) - (3x^2 + 2x - 4y)

Let’s solve this using the two-row format.

4x^2 + 5x
- 3x^2 + 2x - 4y

Since there’s nothing above the 4y, we can put in 0 as a place holder.

Then, let’s do keep-change-change since we have subtraction.

It will look like this now

4x^2 + 5x + 0
+ (-3x^2) - 2x + 4y

After combining the like terms, the answer is

x^2 + 3x + 4y

Now, let’s solve in a horizontal line format

4x^2 + 5x - (3x^2 + 2x - 4y)

Let’s distribute the negative sign into the polynomial in the parenthesis.

4x^2 + 5x - 3x^2 - 2x + 4y

Then, combine like terms.

x^2 + 3x + 4y

And we got the same answer.

Add & Subtract Polynomials 2