 Hey friends welcome again to another session on factorization of algebraic expressions and in the series We are solving a lot of questions so that you become comfortable with problem solving Comfortable with factorization of algebraic expressions So again, we have been given this expression where it is x cube plus 3x square plus 3x minus 7 and We have to you know factorize it right now Have we learned anything where you know or for that matter if you have to approach this What all do we know? We know splitting the middle term. We know how to take commons. We know how to use algebraic identities So can something be used here now if you notice there are two threes here this three and this three and there's a cube term Now if you recall our a plus b whole cube identity was what? Guys a cube plus 3 a square b plus 3 a b square plus B cube is it it now the same thing if it is you know a plus one instead of now B as you know if I keep B as one so what do you get you get a cube plus 3 a square Plus 3 a plus one now. This is where I wanted to draw your attention Right, so a plus one cube is this and now see this is something familiar Isn't it so if I just add one to it it becomes a cube and once it becomes a cube Then difference of cube we have learned so and how to factorize difference of cubes So that's what we are going to take the approach like okay, so x cube plus 3x square Plus 3x and then I simply add one to it right to complete the cube now You'll say if I add one you are changing the expression. Yes, correct We are changing the expression. So hence to compensate. What do I need to do subtract that one from it? Right, so I basically added one and subtracted one so that it becomes same correct and this was minus seven anyways now Advantages that you see this is this becomes x plus one whole cube. How using this this Identity and this one this whole this whole thing becomes x plus one whole cube and this this is minus 8 Now could you sense something? Yes, so this is x plus one whole cube Minus two whole cube two cube now We have already learned how to factorize difference of two cubes, which is nothing, but you take x plus one Minus two then within other brackets x plus one whole squared Minus or other plus x plus one times two plus two squared Is it which which formula folks for a cube minus b cube? My identity is a minus b a square plus a b plus b square isn't it so we use the same thing and Then this is going to help us in factorization So hence x plus one minus two is simply x minus one and here What is it open up the bracket so x square plus 2x plus one x plus one whole square will be written like that This will become 2x plus 2 when you open this bracket up you will get these two terms and then plus 4 Isn't it and it's a matter of surf simplification so x minus one and Square term is only one and 2x plus 2x becomes 4x and My dear friend 1 plus 2 plus 4 is 7 so This is how the factorization would look like Okay, so Mmm Yep, so x minus one x square plus 4x plus 7 so I checked it also. It's absolutely correct Okay, so what did we learn learning is it might not be resembling our standard formats, but you have to be Observant and you can see that You can you bring it to some kind of known format? So what did we do here? We just brought it to the Cube format and difference of cube format and difference of cube. We know how to factorize