 Now in this method of factorization we will look for some terms which can give us a complete square and maybe once we square those terms then or we can we can we get a perfect square of a polynomial then probably we can take some common factors. So let us take an example and understand so first of all let us take this question 4 a square plus or rather let us take 4 4 x square 4 x square plus 12 x y plus 9 y square minus 8 x minus 12 y okay okay so if you observe there are these three terms 4 x square plus 12 x y plus 9 y square is it it looks like they are going to complete a square so how let us let us try and you know do it a little more detailed way so if you see 4 x square plus 12 x y plus 9 y square is nothing but 2 x whole square is it plus and if you see 9 y square can be written as 3 y whole square plus 2 times 2 x times 3 y okay so if you see 12 can be written as 2 times 2 x into 3 y so 2 x whole square plus 3 y whole square like that and then minus 8 x can be written as 4 times 2 x now why did I write like that because you see there is a 2 x here so I am trying to now get as close as to these factors now if you see minus 12 y can be written as minus 4 into 3 y again okay now what is the next step you are very you know you know very close to x square plus 2 times 2 x into 3 y plus 3 y square can be written as 2 x plus 3 y whole square okay and then minus 4 2 x plus 3 y correct so what do you get now you get 2 x plus 3 y common and within brackets you can write 2 x plus 3 y minus 4 correct so hence the factors are 2 x plus 3 y times 2 x plus 3 y minus 4 this is how you converted a polynomial with five terms 2 into 2 factors okay let us take another example another example is this let us say we have x square plus y square minus twice within brackets x y minus x z so there is a another factor x z plus y z okay so hence again what you need to do if you see this is x square y square and minus 2 x y is hidden over here so that will give me an indication to complete the square so it is x square I can write x square plus y square minus 2 x y plus 2 x z again be careful with the sign so minus into minus plus 2 x z and then minus 2 y z isn't it so what is it now so if you see this is nothing but x minus y whole squared right and if you see this is x minus y whole squared and this is an indication that means I must get another x minus y on the from the leftover terms as well so see whether it is possible yes it is very much possible because 2 and z is common in both of them so hence I can write plus 2 z common and remaining factors are x and here it is y so if you see now again we got another common factor x minus y so hence next step will be simply write x minus y so what is left if it was x minus y whole square I took one x minus y so one x minus y will be left over there and if I took away x minus y from here then what is left over here 2 z so hence now the factors are x minus y x minus y plus 2 z so what are the factors x minus y x minus y plus 2 z okay I hope you understood the method