 Now in this question we have to again find a product of two factors so two factors are given this is factor number one and this is factor number two and we have to find out the product one very obvious way is you just multiply the entire term first with the point nine next term and then secondly with this term isn't it so and open the brackets that's what we have learned but then that will be too much you know or lengthy process so what will you do we will now take up the help of algebraic identities again as I keep saying mathematics is all about observation so if you observe again here in this problem what you see is this part and this part are related how if this is a then this is a square isn't it so that's the observation other observation is this part and this part are again related if this is b then here this is b square right and this part if you look closely is nothing but a times b right that's the observation and the moment I know this so this particular and you know given expression you know appears to be like like a plus b and then a square minus a b plus b square isn't it right where a represents what 0.9 x and b represents 0.7 y so if you see the entire expression can be reduced like this yes so what can we say about this then it is nothing but if a plus b a square minus a b plus b square is given you know from the knowledge of algebraic identities it is nothing but a cube plus b cube isn't it so hence let's use that and then so what is a here a clearly is point nine x so hence this particular expression will be reduced to 0.9 x cubed plus 0.7 y cubed isn't now which is nothing but if you see point nine cube is 0.7 to 9 x cubed and it is 0.343 y cubed why because always remember nine cube is 729 and seven cube is 343 so these numbers it's advisable to remember these values because you will be encountering these terms quite often in mathematics okay so this is how we find the product so what did we do we first of all observed what did we observe observed that there is a pattern there is a you know known you know very familiar term terms and hence we used algebraic identities to solve the problem instead of multiplying by opening the brackets we instead used algebraic identity and solved it very quickly