Squaring a binomial (old)

We're asked to simplify 7x plus 10 squared. And your temptation when you see something like this might be to just make it 7x squared plus 10 squared and that would be incorrect. Remember, when you're squaring something, you're multiplying something by itself. So this wouldn't be 7x squared plus 10 squared. This is equal to 7x plus 10 times 7x plus 10. This is not equal to-- sometimes if you said this is 7x times 10 squared, then you could say this is equal to 7x squared times 10 squared. You would be able to do it in this situation right here. But that's not what's going on here. This is 7x plus 10 squared, which is just 7x plus 10 times 7x plus 10. So let me delete that up there. That's probably the single biggest point of confusion when people first learn to take a square of an expression like this. So always remember that it's 7x plus 10 times 7x plus 10. And now we can multiply it out. So one, we could distribute this yellow 7x plus 10 onto each of the terms into the green one. So it would be 7x plus 10 times 7x right here. So we put the 7x out front. And then we could say plus 7x plus 10 times 10. Or we could say plus 10 times 7 x plus 10. I just distributed the 7x plus 10 on each of these terms. Then you do the distributive property again. 7x times 7x is 49x squared. 7x times 10 is 70x. And then you have 10 times 7x is another 70x. And then you have 10 times 10, which is 100. Now, there's something interesting you might want to notice right now is that this expression, it is the first expression squared, right? 7x, the whole expression squared is 49x squared. And then you do have your last expression squared, 10 squared is 100. But then in between, you have the product of these two things twice, and that's just a byproduct of having to do all of the different combinations of products. So the end expression, when you simplify everything, it becomes 49x x squared plus 140x plus 100. So if you want to remember a quick way of squaring a binomial like this, and just remember, it is coming out of this distributive property, but if you had to do it really fast, it's just going to be this first term squared, which is that right there, plus 2 times the product of these two terms. 7x times 10 is 70x, and then you multiply it by 2, you get 140x. You get that right there. And then the last term is just going to be the square of the second term right there. 10 squared is 100.