 in this question we have been asked to expand expand 2x plus 3y whole cube so let's say if you don't have the knowledge of identities then what will you do you will go by the very elementary method of multiplying the three binomials one by one right and you will you will open up these two you'll open up these two brackets first and then whatever is the product you'll get you will multiply with that one isn't it but then we know we have the knowledge of identities and we know that what is the knowledge of identity here so if you see there's a cube of binomial so we have just learned that cube of binomial is given as a cube plus 3 a square b plus 3 a b squared plus b cube isn't it so let's use the same identity and expand it so it will be simply 2x whole cube plus 3 times 2x whole squared times 3y plus 3 times 2x times 3y whole squared plus 3y whole cube right where if you see I have taken 2x as my a and this has become b right so hence if you expand now or simplify it is 8x cube plus this is 3 and this 2 square here this is 2 square right so 3 into 4 12 into 3 36 so it is 36 x squared y right once again 3 and there is a 2x whole square here so after you apply the square 2 square will become 4 so 4 into 3 12 into 3 36 so 36 x square y plus here if you see this 3 will give you 9 because there is a square over here so 9 into 2 18 into 354 so hence we'll get 54 and the powers of x x and then y square and then finally 3 y cube is nothing but 27 y cube right so 8x cube 36 x square y plus 54 x y square plus 27 y cube so this will be the expansion of this now let's take this example so we have to again expand it again if you see this is nothing but a minus b whole cube form which will be nothing but a cube minus 3 a square b plus 3 a b square and minus b cube from our knowledge of identity so as I mentioned earlier also if you have maintained a list of the identities and then you can refer to those that list and if you see this will be the expansion of a minus b whole cube so here if you see this one will be treated as a and this one will be treated as b so hence the expansion would be nothing but a cube that is 1 by 3 x whole cube correct because a is 1 upon 3 x minus 3 a square so 1 by 3 x whole squared times b b is 2 upon 5 y plus 3 times 1 upon 3 x into 2 upon 5 y whole squared minus 2 upon 5 y whole cubed isn't it now it's reduced to only or it's left to just simplify them so this will be nothing but 1 upon 27 x cube right minus 3 times 1 upon 3 x square will be nothing but 9 x squared I can write that into 2 upon 5 y so let it be like that then plus 3 into 1 upon 3 x into 4 upon 25 y square if you open the square here you'll get this and minus 2 cube is 8 and 5 y is 125 y cubed right so can we simplify a little bit yes we can so if this 3 and this 9 will get reduced this 3 and this 3 will go so hence final answer will be 1 upon 27 x cube minus 2 upon 15 x squared y so this 3 goes and multiplies with this 5 right then plus 4 upon 25 x y squared x y squared so this x y squared and minus 8 upon 125 y cube so what did we do we simply applied this identity and expanded the given expression