 So it's useful to remember that while we can always attempt trial and error factorizations, there are some special products that are easy to factor. And if you recognize when you have a special product, it's much easier to factor. For example, if we expand A plus B squared, we find the product is A squared plus 2AB plus B squared. And this gives us a very specific form. Notice that this product is the sum of two perfect squares plus twice the product of the square roots. And so if we ever run into any expression that is the sum of two perfect squares plus twice the product of the square roots, we know that it's the square of a binomial. Well, the first thing to check is to see whether we have the square of a binomial. So is 4x squared plus 9y squared plus 12xy the square of a binomial. So remember the square of a binomial has a very specific form. And so we want to see if our expression has the same form. And so we might notice that 4x squared is the square of 2x. 9y squared is the square of 3y and 12xy is 2 times the product of the square roots, 2x and 3y. And so we have the square of a binomial and that's going to factor as A plus B squared, 2x plus 3y squared. So let's try to factor. Now in the real universe math problems drop out of the sky with instructions on how to solve them. Oh wait, they don't. So we do need to check. Let's see if we can use this new fangled tool of the square of a binomial. And so remember we require that we have the sum of two perfect squares and twice the product of the square roots. So well this 25x squared looks like it might be a perfect square so let's see if it is. And it is in fact the square of 5x. We have these other two terms. 10x doesn't look like it's a perfect square but maybe 1 is and so we find. And so 1 is 1 squared, a perfect square. And now for the check, the remaining term, 10x, that needs to be 2 times the product of the square roots, 5x and 1. And so we should check it. And it is. So we have the square of a binomial and it's going to factor as a plus b squared. 5x plus 1 squared. How about something like this? Well to begin with remember that when we find the square of a binomial we have a bunch of added terms. So we might want to rewrite this as 18x squared plus minus 24x plus 8. A useful thing to begin with is to always start by removing any common factors. And we see here that all of these terms are even so they all have a factor of 2. So let's remove that common factor and now let's see what we have. So we notice that 9x squared is a perfect square. Minus 12x doesn't look like it'll be a perfect square, but 4 has possibilities. And then minus 12x, well that's 2 times the square roots, 3x and 2. Oh wait, that's not true. However, all is not lost. Remember that every real number has 2 square roots, 1 positive and 1 negative. So if we use 4 as minus 2 squared and change our other square root here, then minus 12x is 2 times the product of the square roots, 3x and minus 2. And so this is the square of a binomial. And that means we can factor, it's the square of the sum of the square roots, 3x and minus 2. So let's try to factor 4x squared minus 20x plus 9. And so we notice that 4x squared is a perfect square. 9 is a perfect square. And minus 20x is 2 times the product of the square roots. Oh wait, 2 times 2x times 3 is positive so we'll make that 3 a negative 3. And so minus 20x is 2 times the product of the square roots. And so 4x squared minus 20x plus 9 will be the square of 2x minus 3. And not quite. Remember when you write equals, you are guaranteeing left-hand side and right-hand side are identical. And minus 20x is not 2 times 2x times minus 3, which means that this is not the square of a binomial. If it factors, we'll need to use trial and error. And the important thing to remember here is that we can always attempt trial and error factorization. And sometimes we have to.