 In this problem we have been asked to simplify the given expression. Now here there are two parts one is a two factor expression another is a binomial cube so as we see it is you know the the second part is a clear indication that we are going to use algebraic identity right and this part also again if you observe this is square term right so 6 m square is 36 m square and n square n square is n square here right so hence what kind of identity would be this is nothing but a minus b times a square plus a b plus b square so we check a b is 6 mn actually so hence this perfectly fits into this setup so hence we know this is nothing but a cube minus b cube so this will help me in reducing this to what tell me it will be nothing but 6 m cube whole cube minus n cube is it and the other one this one this one you know how to expand this you know this a plus b whole cube is nothing but a cube plus 3 times a square b plus 3 a b square plus b cube isn't it remember the identity if not as I have told you keep a list of all the identities and fix it in front of your study table or wherever you study and then whenever you are solving such problems do refer to this list do not try to mug up why because let enough practice help you remember those identities okay now so if I expand if I expand that there's a minus sign here and within practice I can write 3m cube 3m cube plus 3 times 3m square now this dot represents multiplication don't confuse it with decimal dot 2n that means multiplication of 2n and then plus 3 times 3m dot 2n whole square plus 2n whole cubed isn't it let's simplify them further so it is nothing but 6m cube so if you see 6 cube is 2 1 6 correct so 2 1 6 m cube minus n cube and then within brackets I will get 3m cube is 27m cube then if you simplify this you will get plus 3 into 9 into 2 54 right 54 m square n then plus 3 into 3 into 2 square that is 4 so 3 3s are 9 9 4s are 36 m n squared plus 8 n cubed isn't it now simplify it further so if you see it will you'll get 206 m cube minus n cube minus 27 m cube minus 54 m square n minus 36 m n square minus 8 n cube okay so hence if you see there are like terms what are the like terms here these are the like terms and there's another set of like term this one right so if you simplify them you will get 216 m cube minus 27 m cube is 189 m cube then minus m cube minus 8 n cube will be minus 9 n cube and remaining terms as it is because there are no more like terms isn't it so this is the most simplified form of the given expression this happens to be a cube cube right this is how you have to solve this problem