 Hi and welcome to the session. Let us discuss the following question. Question says, show that 9p minus 5q whole square plus 180pq is equal to 9p plus 5q whole square. Let us now move on to the solution. First of all, consider left-hand side of the given equation. Left-hand side is 9p minus 5q whole square plus 180pq. Now recall the identity which states that a minus b whole square is equal to a square minus 2ab plus b square. Now compare this square with the left-hand side of the identity. Generally you can see value of a here is 9p and value of b here is 5q. Now substituting 9p for a and 5q for b on right-hand side of the identity, we get 9p minus 5q whole square is equal to 9p raised to the power 2 minus 2 multiplied by 9p multiplied by 5q plus square of 5q and this term that is plus 180pq is as it is. Now this expression is further equal to square of 9p minus, clearly you can see 2 multiplied by 9 is 18 and 18 multiplied by 5 is 90. So product of these three terms is 90pq. Multiplying constant terms we get 90 and multiplying variable terms we get pq. Now this plus sign is as it is and here we write square of 5q. Now this 180pq is as it is and we have written this plus sign as it is. Now rearranging the terms of this expression we get 9p whole raised to the power 2 plus 5q whole raised to the power 2 plus 180pq minus 90pq. Now note that these two terms are right terms. So we can subtract them easily. So we write square of 9p as it is, this plus sign is as it is. Now again this term is as it is and difference of these two terms is 90pq. Clearly you can see pq is common in both these terms. So here we can take pq common and 180 minus 90 is left inside the bracket. Now difference of 180 and 90 is 90 so we get 90pq. Now again rearranging the terms of this expression we get square of 9p plus 90pq plus square of 5q. Now this expression can be further written as square of 9p plus 2 multiplied by 9p multiplied by 5q plus square of 5q. Clearly you can see here that 90pq is equal to product of 2, 9p and 5q. So here we have written 2 multiplied by 9p multiplied by 5q for 90pq. Now recall the identity which states that a plus b whole square is equal to a square plus 2ab plus b square. Now compare the right hand side of this identity with this expression. Clearly you can see here 9p represents a and 5q represents b. So using this identity we get this expression is equal to 9p plus 5q whole square. Clearly you can see we have obtained this square by substituting 9p for a and 5q for b in left hand side of this identity. Note that right hand side of the given equation is 9p plus 5q whole raised to the power 2. So we get LHS that is 9p minus 5q whole square plus 180pq is equal to 9p plus 5q whole square that is RHS. Hence we have proved the required result. This completes the session. Hope you understood the solution. Take care and bye for now.