 Hello friends, so in this question we have been given that a plus b plus c is 9 and a b plus b c plus c a is equal to 40. We have to find out the value of a square plus b square. So the moment we see such questions, first thing is this is a trinomial and we are expected to find out the value of square of the individual terms. So clearly it indicates that we have to use the trinomial expansion, trinomial square expansion so we know that. So let's start the solution. So let us say a plus b plus c is equal to 9. So squaring both sides, squaring both sides, what will you get? You will get a plus b plus c whole square is equal to 9 square. Isn't it? This implies if I expand the identity I will get a square plus b square plus c square plus 2 a b plus 2 b c plus 2 c a is equal to 81. 9 square is 81. Now if you notice this is what we are expected to find a square plus b square plus c square. So can I not write a square plus b square plus c square is equal to a 81 minus 2 a b minus 2 b c minus 2 c a. So if you see this is nothing but 81 minus. If I take 2 common, minus 2 common so it will be a b plus b c plus c a. Isn't it? Which reduces our effort to almost nil now because I know that this value has been given and this value is nothing but 40 over here. So hence it is 81 minus 2 times 40. Hence it is the value of a square plus b square plus c square will be simply 1. So this is the answer. So what is the learning? We implemented or applied this a plus b plus c whole square trinomial and the moment it was asked to find out a square plus b square plus c square remember that you have to deal with the trinomial square identity and that is how we solve this problem.