 Another special product is the product of a sum and a difference. If we expand a plus b times a minus b, we find and these two mixed terms, a, b, and minus a, b, will cancel each other out. And so we'll end up with a squared minus b squared. So the thing to notice is that in our expanded form, both of the terms are squares and they're subtracted, and there is no other terms. And so that we say that we have a difference of squares. For example, let's try to factor for x squared minus y squared. And so we notice our first term for x squared is a square of 2x. And our second term, y squared, well, that's the square of y. And they are subtracted. So we do have a difference of squares and that will factor as the sum and difference of the square roots 2x and y. So this will factor as 2x plus y times 2x minus y. Or we might take 25x squared minus 16. And so we see that we have two perfect squares and they're subtracted. So this will factor as the product of the sum of the square roots, 5x plus 4, times the difference of the square roots, 5x minus 4. Or we could have something like x squared plus 4. And so we have two perfect squares and they're subtracted. So we have a difference of squares. Wait, no, that's a plus. They're not subtracted. So this is not a difference of squares. Well, that's OK. This must be the other thing. So we notice that x squared is a square, 4 is a square, and that middle term, well, it's a 0x. And so it's 2 times the product of the square roots. And so this is the square of a binomial. Oh, wait, that's not true either. Again, only right equals if you're willing to commit to saying the left-hand side and the right-hand side are the same thing. And so we do not have the square of a binomial. And what this means is we need to use trial and error factorization. Now, since we want our constant terms to multiply to 4, the only numbers that multiply to 4 are, and so the only hopes for factorization are either that x squared plus 4 is x plus 1 times x plus 4. So we'll check it out. Nope. Or maybe x squared plus 4 is x plus 2 times x plus 2. So we'll check it out. And no. And since these were the only possible factors, this means that no factorization is possible.