Subtract y2+3y−4y^2+3y-4 from 6y2−7y+96y^2-7y+96y2−7y+9.

5y2−$$10y+135y^2-10y+135y2$$−10y+13

Subtract y 2 + 3 y − 4 y^2+3y-4 from 6 y 2 − 7 y + 9 6y^2-7y+9 6 y 2 − 7 y + 9 .

Folks, so let's take a look at our next practice problem. We're going to try to set it up very similar to the last one that we just did. We've got these two polynomials and instead of the symbols already being written for this, we just have a sentence. We're going to subtract y squared minus plus three y minus four from six y squared minus seven y plus nine. We want to be able to write these things vertically instead of side by side. How do we do that? Well, we're going to follow a very similar format, but there's one sort of key distinction here. We're subtracting this polynomial from the second one. So, when we go to write these things vertically, we actually want to start out with writing the second one on top. This is sort of like a linguistic difference. We're subtracting one polynomial from another instead of adding one to another, So, the order actually matters here. We want to write this one on top because we're subtracting this one minus this one. Okay. So, all that really means here is we're going to start off with our six y squared minus seven y plus nine and the idea is the same. I want to be able to stack or align like terms vertically so that it just makes the addition or subtraction much more straightforward. I'm doing subtraction in this case, so I'm going to put a minus sign over here and then we just again are going to align the terms from the first polynomial to kind of fall in line. So, what about the y squared term? This is going to be written right over here. And then about the y term, so this is going to be the three y, and then I've got the constants in the first polynomial which is a minus four. You're going to keep that minus sign there. Alright, so now what happens here is I can just draw the line and I can start to do the subtraction vertically. So, what if I take six y squared minus y squared? What is the result of that? I just get five y squared. Alright, so five y squared is going to be the y squared term. What about this over here? I've got negative seven y, and then I've got minus a positive three y. So, I've got negative seven minus three. What does that become? Well, negative seven minus three becomes negative 10 y. Just pay attention to the signs here because the signs matter. If this were a negative sign, then I would have had to subtract a negative, which is the same as adding, but that's not what happened here. Okay? And then finally, I've got a plus nine, then we've got a minus negative four. So, that's exactly what I was just talking about. Here, we're subtracting a negative four. So, this is the same thing as adding four. So, now what happens is I'm subtracting negative four, so that's nine plus four, which becomes 13. Alright? So, just be really careful about when you do signs like this, especially in subtraction type problems. This is really all there is to it. So, this is the final answer. We've got five y squared minus 10 y plus 13. Again, you can go ahead and double check this by grouping these things together sort of side by side, and you'll see that it works out to this. Let me know if you have any questions. Thanks for watching.