 Hello friends welcome again to problem solving session I hope you are doing the problems and going through the solutions which I have provided on the channel and you are also practicing with enough number of questions on the reference book right now in this question we have got a plus b equals to 7 and a b is equal to 12 so two values are given you have to find the value of a cube plus b cube and a square minus a b plus b square again so what will be the approach in such questions you know the moment a few linear term values are given so a plus b is a linear term clearly its value is given as 7 and a b is given as 12 so we have to arrive at the value of a cube plus b cube now obviously we it gives us a hint that we have to use an algebraic expression where a cube and b cube are related to a plus b as well as a b isn't it and that kind of a relation we know it's nothing but a plus b whole cube is given as what a cube plus 3 a square b plus 3 a b square plus b cube here if you simplify it further you'll get a cube plus b cube and if you take three a b common between these two terms you'll get three a b times a plus b is it another form of the cube of a binomial so my dear friends a cube plus b cube can be rearranged on the left hand side to get what you will get a plus b whole cube minus 3 a b a plus b so basically I have taken this entire term left hand side and just swap the position of left hand side and right hand side to get this particular relationship now very easy so you know how to find out the value of a cube plus b cube a plus b is 7 so 7 cube minus 3 times a b is 12 times a plus b is 7 again so you will get 7 cube is 343 minus 3 into 12 into 7 is 25 so the final value is 91 okay now let us find out a square minus a b plus b square the b part this one how to do that we know another identity where this is involved so what is that we know that a cube plus b cube is nothing but a plus b a square minus a b plus b square guys you need to remember these identities you know it should be you know by hearted now so when I know this and I have already figured out the value of a cube plus b cube a plus b value is given so I can find out a square minus a b plus b square so what is it a square minus a b plus b square would be nothing but a cubed plus b cube divided by a plus b isn't it and what was a cube plus b cube if you see in the previous question we found out a cube plus b cube was 91 and a plus b was given to be equal to 7 right a plus b was 7 so hence what is it a cube plus b cube divided by a plus b which will be equal to nothing but 13 right so 13 is the answer 13 is the value of a square minus a b plus b square