Subtracting Polynomials 04:59 minutes

Video Transcript

Transcript Subtracting Polynomials

Ross is very much in love with his girlfriend, Raquel. For her birthday, he wants to give her something made with love. He found an old frame in his garage that he wants to fix up so he can frame a picture of himself to give to Raquel. In order to revamp the frame, he decides to order some scraps of fabric online.
The website offers various sizes of fabric. Ross needs to measure the frame before he decides how much fabric to buy. He needs to be careful because he doesn't want to include the space the picture will occupy in his measurements.

Polynomial Subtraction

To find the size of the frame, Ross can use polynomial subtraction. While browsing a do-it-yourself blog, Ross finds two formulas to use. y₁ = 2x² - 8x represents the area of the frame, including the picture. And y₂ = x² - 2x - 8 represents only the inner area of the frame. In order to find the area of the frame without the picture, Ross needs to subtract the area of the picture (y₂) from the area of the whole frame (y₁).

Vertical Method

There are two methods for doing this. First, let's do the vertical method. Make sure the polynomial expressions are in standard form. This means that the terms are in descending order according to their degree. Here they are.
When we subtract a polynomial, we need to make sure we subtract all of the terms. To do this, we need to distribute the minus, which is the same as multiplying by -1, to each term. Now we can add or subtract term by term according to the signs.
2x² - x² equals x². -8x +2x equals -6x, and because we don't have a constant in our first equation, we can add 0 plus 8, which equals 8. Ross just has to plug in the width of his frame for 'x' to find out how much fabric he needs.

Horizontal Method

Another way to subtract polynomials is by using the horizontal method. Again, first make sure that they are in standard form. We can distribute the subtraction sign to all terms inside the parentheses, just like we did before. So that gives us 2x² - 8x - x² + 2x + 8. Now we can rearrange the order so that all of the like terms are next to each other, horizontally. 2x² - x² simplifies to x² then -8x + 2x combine to make -6x. 8 does not have any like terms to combine with, so we will just bring plus 8 down. The resulting answer is x² -6x +8.

Adding Vertically

Let's look at one more example. When adding vertically, put the expression in standard form, then make sure that all of the like terms are lined up together. Here we'll need to move the +2 so that it's above -4 because they're both constants. After combining like terms, you end up with 2x² +2x-2.

But be careful! Sometimes you have polynomials that look like this. The first term has a combination of variables. It may seem like you can combine it with the other two terms but you canNOT. When combining terms, the variables need to look alike. They must have the same combination of variables and each variable must be raised to the same degree.

Alright, now that Ross has finished the frame he gets to give it to his girlfriend Raquel. But she isn't as excited as he thought she would be...because now she has 121 framed pictures of Ross...