Multiply the polynomials using special product formulas.(3x+5)(3x+5)\left(3x+5\right)\left(3x+5\right)(3x+5)(3x+5)

9 x 2 + 30 x + 25 9x^2+30x+25 9 x 2 + 30 x + 25

Multiply the polynomials using special product formulas. ( 3 x + 5 ) ( 3 x + 5 ) \left(3x+5\right)\left(3x+5\right) ( 3 x + 5 ) ( 3 x + 5 )

Hi, everyone. So in this practice problem, we have the polynomials 3x+5 times 3x+5, and I wanna multiply these by using some of our special product formulas. Again, I've got them over here just for reference, but the whole idea is the same. I wanna take this left side over here, and I wanna see if I can match it to one of the things on the left side in these formulas because then I'm done. And if I can figure out and identify the pattern, then my answer is just gonna be whatever's on the right side. So let's take a look. I've got 3x+5 and 3x+5. So is this of the form a+ba? Well, you might think so, but it's very, very close. What happens is I have a 3x+5+5. The difference of squares formula only worked when you had something like+5 in 1 and minus 5 in the other. So if this was a minus, then this would have been a perfect square. Instead, what happens is I can actually rewrite this expression. Remember, if you ever have the same thing that's multiplied by itself, we can use exponents for that. So another way to rewrite this expression is it's really just 3x+5 squared. So what happens here is I've taken this expression, and I've written in a way where now it actually does look like something that I've looked at in my special formulas. It looks like a plus b squared. So the whole idea is that sometimes you might see expressions that don't immediately look like the left side, but you can manipulate them so that they do. So this is 3x plus 5 squared. And so what that means is I can basically use this sort of formula over here. So what I've got here is I've got a plus sign, and this might look a little bit different from how we looked at it in the video. Basically, this is just a more compact version of what we saw. If you have a plus sign here, then the first sign is plus. If you have a negative sign here, then the first sign is negative, and the second sign is always positive. Okay? So I have a plus sign here, which means I'm gonna use the sort of plus version of this. This means I do a squared actually, I'll put this down here. I have a squared plus 2ab, and then plus b squared, because this really is of the form a+2. Alright. So I'm basically done. This is what my formula is gonna look like on my right side. All I have to do is actually just figure out what the a's and b's and a squared and b squared are. So let's do that over here. What is a in this expression? So I've got 3x+5squared. So notice how my a is 3x, and in this case, my b is equal to 5. Okay. So what does that mean? It means that I have to compute a squared to b squared now. So if you do a squared, a squared is 3x times itself. So the 3 and the 3 become 9 and the x becomes x squared. And then the 5 over here is pretty straightforward. This just becomes 25. So 5 squared is 20 or b squared is 25. Now I basically just pop it into this expression over here, and I'm done. Alright. So a squared just becomes 9x squared, so that's 9x squared. Then I've got 2ab. So 2ab is 2 times a, so this is 2 times 3x over here, and then b is equal to 5. So you have to compute all of those things, plus, and then I've got to do b squared, which is 25. Alright? So what I wanna actually do here is I'm just gonna, like, sort of write this over here. I'm gonna bring this down, and this really just becomes 9x squared plus 2 times 3x times 5. Do the 2 times 5, which is 10. 10 times 3x would be 30x. And then over here, I just have 25. And that is my expression. So here I've got this polynomial that I've squared, gets a little bit more complicated when you have things in, like, you know, your a and b aren't just like x's and stuff like that. Right? But that's how to do this. Let me know if you have any questions. Thanks for watching.