 Hey, hi friends, welcome again to another session on problem solving on quadratic equation. Now here we have been given to solve quadratic equation by the factorization method. So what is the difference between this particular question and whatever we have been doing so far? So if you see we have some, you know, non constants here. So though, you know, 2a and a square minus b square represent constant, so what I meant was they are not numeric, they are not numeric, right? So earlier you saw examples like x square minus 3x plus 2 equals 0 and you are asked to solve this using factorization method. But in this question, coefficients are non-numeric. So hence, how to go about it? It is again, you know, spreading the middle term is what we are going to adopt. So spreading the middle term, how did it work? So basically you had an equation ax square plus bx plus c equals 0 here. I am purposefully using capital A, B and C to avoid confusion with let's say the a's and b's here. So a is the coefficient of x square, which is here if you see is 1, b is the coefficient of x, which is here minus 2a and c is nothing but a square minus b square and what was the methodology? We used to multiply a and c first, right? So a and c, if you multiply, you will see 1 into a square minus b square, right? And then we have to split b in terms of b1 plus b2 such that b1 b2 is equal to ac. That's what we have to do. Now ac clearly is 1 times a square minus b square and I told you, you factorize ac first. So you factorize, it's clearly nothing but a minus b, a plus b2 factors are there, correct? And now b1 b2 should be such that the product is ac. So if you see, if I consider this to be b1 and this to be b2, then it is suiting our requirements. So hence, why? Because if you see add b1 plus b2, you will get a minus b plus a plus b, which is nothing but twice of a, which was not here. If you see, it's here. So hence, let's split like that. So what will I do? I will write x squared, then minus a, a can be written, 2 a can be written as minus ax minus ax, isn't it? Minus ax and minus ax, that's how, or other, no, not like that. So basically, you can say x square, then a minus bx, then minus a plus bx, isn't it? If you see, I split the middle term like this, into a minus b and a plus b. Some of these two terms is minus 2 a clearly. And the c term, the constant term is a minus b, a plus b. And this is equal to 0. Now clearly, if I take x common from these two, so let's take x common, so x common and it will be x minus, within brackets, a minus b, isn't it? And in the last two terms, you can take a plus b common. So if you see a plus b and x, sorry, only a plus b common, so what will you get? You will get x minus a minus b. And this is equal to 0. And thankfully, we have another set of common factors here. So you can pull that out. So it is like that. And then within brackets, this x will come here. And this thing will come here. So minus a plus b. And this is equal to 0. So now the usual method, we liquid each of the two terms, linear terms to 0. So you'll get x minus a minus b as 0. And x minus a plus b as 0. So hence, x is equal to a minus b and x is equal to a plus b. These are the solution to the given quadratic equation. So hence, if the coefficients are non-numeric, then you have to use the concepts of algebra to factorize the AC. The usual method of splitting the middle term should be used to solve the equation.