 In this question it's given that x minus y is equal to 4 and value of xy is 21 and you have to find out the value of x cube minus y cube. Again in such problems what should be the approach? If you see linear terms and in there here it is xy is equal to 21 is given and x minus y is 4 is given. Now I have to come to from this expression we have to lead to this particular expression. How to do that? So you see there is an indication there is a power 3 both are having power 3 that means it is kind of indicating that you could find something with this operation that means if I raise both the expressions to power 3 I will definitely get some terms in the expansion which will be x cube minus y cube. So let us see whether that helps so we have been given x minus y is equal to 4 isn't So you know raising both sides to power 3 we will get x minus y whole cube is equal to 4 cube very good and now we know x minus y whole cube by our identity knowledge we know this is nothing but x cube minus 3 x square y plus 3 x y and sorry x y square and minus y cube and this will be 64 4 cube is 64. Now we have learned one you know arrangement if I I have to basically find these two isn't it so let us see what is it so x cube minus y cube is what we expect and rest everything should be transferred on the other side so it will be 3 x square y minus 3 x y square so this goes on the other side becomes negative this goes on the other side becomes positive so that's what I have done here now if you see closely this is nothing but 64 and there are few terms common in this guys isn't it so I can take 3 x y common and it becomes x minus y is it so what will it become it is nothing but 64 plus 3 times x y x y was given as 21 you see here and x minus y again I can use it as 4 hence the value should be 64 plus 12 times 21 is 252 isn't it so hence the value will be nothing but if you add both of them you will get 3 1 6 so this should be the answer x cube minus y cube should be 3 1 6 so learning is the indication we went by our indication or you know the feel which was coming as in if there was a cube here so that you know in a way they are asking us to cube the binomial so if you cube the binomial I will get this term that's what we did in this question again if you see there is given that x plus 1 by x is equal to 7 so you have to find the value of x cube plus 1 by x cube if you see again it is hinting us to go for a cubing of the binomial so let's do that so if I do x plus 1 by x whole cube I will get 7 cube so let's expand using the identity which with us is a plus b whole cube is equal to a cube plus 3 a square b plus 3 a b square plus b cube right so let us use that so it is nothing but x cube plus 3 times x square times 1 upon x plus 3 times x times 1 upon x whole square plus 3 times sorry and the last term will be simply 1 upon 1 upon x whole cube and this is 7 cube 7 cube is 343 okay so 7 cube is 343 now what so if you see what we can do is let us first club together what do we desire so we want this so x cube plus 1 by x cube is clubbed together now again you can take some common terms here isn't it so if you see this is nothing but 3 is common x is common and 1 by x is also common and leftover is x here and here 1 by x correct and this is equal to 343 now this x and this x goes and we already know x plus 1 by x value that is 7 so hence x cube plus 1 upon x cube plus 3 into 7 is equal to 343 so hence x cube plus 1 upon x cube will be equal to 343 minus 21 which is equal to 322 so x cube plus 1 by x cube is 322