 Hey friends, welcome again to this session on factorization and there is a new question here. We have to factorize x to the power 4 plus 4x square plus 3. Now the moment we see powers like 4 and all, it gives us a lot of trouble retention, is it? So how to, we have never seen such kind of expression, so how to resolve it? So always remember x to the power 4, whenever you see such expression, it is nothing but x squared squared, isn't it? If you keep this in mind then it becomes much easier. So hence, can I express this as x squared squared plus 4x squared? Now, why is 4x squared given here and why is this 3? So there must be some reason, right? And so let's understand what's the reason. So the moment I see this squared, I am tempted to convert this into 2ab form. So if you see, so what I mean is, this looks like a square, isn't it? If you consider a to be x squared, then this looks a square plus this 4x square, I am tempted to write this at a2 into a into 2, isn't it? 4x square where x square is a, keep this in mind and this 3, correct? Now again, coming back to our original expression, we can write this as x squared squared plus 2 times x squared times 2, isn't it? Now I will stop here and I will keep this plus sign open so that we don't forget to write 3 later on. But then let's stop here and analyze this particular expression, this one and this one. It looks like it is a square plus 2a into 2, where a square plus 2ab, so b is 2, isn't it? So if I somehow get 4 or 2 square here, then this becomes a perfect square, isn't it? And why am I doing it? You will get to see the moment you see, you know, the next steps. So I need to have 4 here, I need to have 4 here. But my dear friends, only 3 was given, only 3 was given. That means I have to compensate this 4 by subtracting 1, right? So 4 minus 1 is 3. Now you have to change your perspective and look these 3 terms together. So what is this? This is x square square plus 2 times x square times 2 plus 2 square, right? And then minus 1. This minus 1 will tell you how to use it later on as well. But right now, it's nothing but x square plus 2 whole square, isn't it? And minus 1 now can be written as my friend 1 square. And this is what we intended to find. Why? Because now this is difference of, difference of 2 squares, my friends, okay? So difference of 2 square. So I know what is difference of 2 squares. If a square minus b square is difference of 2 square, it can be factored into a minus b times a plus b. So let's use it, where this entire item is a, 1 is b. So hence we can write x square plus 2 minus 1 and here it will be x square plus 2 plus 1 guys. So hence what is it? x square plus 2 minus 1 is plus 1. And x square plus 3, so if you see, we got x square plus 1 times x square plus 3. This is these are the 2 factors. So hence what is the learning in this problem? The learning is do not panic when you see powers like 4 and all. The moment you see 4 what should come to your mind, it is nothing but square of something. And when you get 1 square term, then you always remember 1 square term must be, you know, complemented with some other square term to complete the square. And in this case, that was here this 4 and the 2 xy, 2 ab form, right? And we completed the square, we got a full perfect square and we somehow wanted to reduce it to difference of 2 squares which we fortunately got. And the moment we got difference of 2 squares, we know how to factor that, right? This is what is the learning of this problem. So keep that in mind and try more such sums to make it more clear.