 Hello friends, welcome again to this problem solving session. So we were doing problems on cubes of binomial and this is another question related to that. So the question says basically we have to find the product of this. So we have to find calculate the product or evaluate the product, how to find out the product of these two terms. Obviously this second term looks a little intimidating but no worries we'll try and figure out a trick to solve such questions. Now mathematics is all about you know keen observation. So hence if you are really observant you'll be able to solve problems very easily. Now if you see very closely there are some patterns here. So I can see 7a and 7a square is 49a square isn't it? Similarly if you see 5b, 5b square is 25b square. Does it indicate something? So have we learned algebraic identity where there are two terms in the first factor and three terms in the second factor. Hence I have already urged you to maintain a list of identities and keep that list of identities in front of your study desk and whenever you're solving algebraic identity related problems you should be referring to that list. So if you check that list you will see that there is an identity which says a minus b times a square plus a b plus b square is given as a cube minus b cube. Right so we are going to use this identity here. Understood? So what was observation here also a and a square here. So if you see a and a square and here b and b square and this middle term has to be product of a and b. So let's check whether we can express the given problem into this particular form. So I can write this as 7a minus 5b and then I can clearly write 49a square as 7a square. Let me put it in within square brackets to differentiate and then here it is 7a into 5b. Now how did I know this? So again as I told you it's an all all about observation. So if you see 5b is there so hence to get this identity I have to get this term a square plus a b plus b square. So a square I have got so 7a and 5b will be the next term so that the third term becomes 5b whole square. Now this matches with our identity so this is our a so this is a this is b this is clearly a square this is a times b and this is b square isn't it? So we have got our identity so hence what will be the product? Very easily product will be nothing but so product we know is a cube minus b cube so 7a cube minus b cube so b in this case is 5b. So b in this case is 5b. Now don't get confused between these a and b's here and here it is 7a and 5b. Now a and b is symbolic over here. a represents whole of this this is a this is a representation here so this a here is of this identity and this a represents 7a. Similarly this b represents 5b so hence it could be any other thing as well so hence whenever there is and let us say this is like star and delta so star minus delta star cube minus delta cube will be equal to star minus delta times star square plus star times delta plus delta square now star and delta could be anything right couldn't be anything so hence just a symbol right so hence if star is here is 7a and delta is 5b so hence you know this is nothing but star cube minus delta cube right so without actually doing any multiplication we arrived at the result that's the beauty of algebraic identity.