 This video is called Solve by Factoring 2. There are two problems in this video and they are both what are considered difference of squares. We have talked about this in previous videos where you can remember the difference of squares is if there's a subtraction sign between two terms. Now notice the 9 is a perfect square and so is the 121. This problem is really asking 9x squared plus 0x minus 121 equals 0. And the nice shortcut what will always work is when you have the subtraction sign in perfect squares you can use the square roots. So let's break up the x squared into x and x. Sorry I didn't leave much room there. The 9 squared of 9 is 3 so you can do the 3 and the 3 and then what's the square root of 121? It will be 11 and 11. Since it's the minus and we want them to add up to a 0 you'll do plus 1 minus 1. Now if the problem just said factory and you'd be done but remember this is a solve by factoring problem we have the equals 0 here. So we have to take both of our terms and set them equal to 0. 3x plus 11 equals 0 3x minus 11 equals 0. So we subtract 11. I get 3x equals negative 11 divide both sides by 3 I get an x equals negative 11 thirds. You could change it to a decimal if you wanted but you might as well just keep the answer like that. Same as over here we add 11 3x equals 11 you divide both sides by 3 you get x equals a positive 11 thirds. So that tells us that if we were to graph this parabola this u shaped curve well it would cross at 11 thirds which is between 3 and 4 it's almost at 4 and a negative 11 thirds which is between negative 3 and 4 negative 4. So it looks something like that. Let's try one more example. Now we know that this is going to be a parabola because the x squared tells us it's going to be a u shape and it wants us to solve by factoring but remember there's one thing we have to do before we can start taking out a GCF and that is everything has to be on one side of the equal. Right now I've got things on both. So before I start factoring let's subtract that 81 over we get 16x squared minus 81 equals zero. But now something popped up. I've got a difference of squares. I've got a negative and both of my numbers here are perfect squares. So remember that's really asking me what 16x squared plus 0x minus 81 is but because it's a difference of squares we don't have to spend all our time making the lists and guessing and checking we simply can take our shortcut. The 16x squared will be 4x and 4x. The 81 is 9 and 9 and since it's a difference of squares remember you need one positive one negative. Now if this was simply a factor problem we'd be done but it's not. It's a solved by factoring. We've got the equals zero so we have to take both of our terms and set them equal to zero. So I have 4x plus 9 equals zero and 4x minus 9 equals zero. So to solve both of these 4x equals negative 9 when you divide both sides by 4 you'll get x equals a negative 9 over 4. When I add 9 4x equals 9 and I divide both sides by 4 I get x equals a positive 9 over 4. So these would be both of my answers.