 the difference of two squares. What do you notice in these four products? The first product is x squared minus x plus x minus 1. These two terms collapse and you get x squared minus 1. Here you get x squared minus 2x plus 2x minus 4 again the two middle terms collapse and you get x squared minus 4. Here you get x squared minus 3x plus 3x minus 9. Middle terms collapse this is x squared minus 9. So you expect the same pattern here. You're gonna have x squared minus 16. So what is x squared minus 25? Well it must be, it must factor as x plus 5 times x minus 5 which you can readily verify. What about 9x squared minus 4? We have to take the square of this first term. Let's see, it looks like it should be 3x plus the square root of 4 2 times 3x which is the square of the first term minus 2. Let us check. This is 9x squared minus 6x plus 6x minus 4. Does it collapse? Yes indeed. That is what we're looking for. And in general when you have the difference of two squares they factor as the square root of the first term a plus the square root of the second term b times the square root of a squared which is a minus the square root of b squared which is b.