 Hi and welcome to the session. I am Asha and I am going to help you with the following problem that says use suitable identities to find the following products. So first let us learn the identity with the help of which we will solve the following problem. Suppose we have two binomials x plus a and x plus b then their product is equal to x square plus a plus b into x plus a into b. So this identity is a clear idea with the help of which we will find the product of the following given problems. Let us now start with the solution and the first one is x plus 4 into x plus 10. Now on comparing this with the left hand side of the identity we find here that a is equal to 4 and b is equal to 10 and on applying this identity x plus 4 into x plus 10 can be written as x square plus a plus b that is 4 plus 10 into x plus a into b that is 4 into 10 which is further equal to x square. 10 plus 4 is 40 in x plus 4 turns up 40. Hence the product of x plus 4 and x plus 10 by using a suitable identity is x square plus 4 in x plus 4 t. So this completes the first part. Now proceeding on to the second part where we have to find the product of x plus 8 and x minus 10. Now on comparing it with the left hand side of the identity again here we find that a is equal to 8 and b is equal to minus 10 and thus on applying the identity we have x square plus a plus b a is 8 and b is minus 10 into x plus a into b that is 8 into minus 10 which is further equal to x square plus 8 plus minus 10 is equal to minus 2 into x plus 8 into minus 10 is minus 8 t. It is further equal to x square plus into minus is minus so minus 2 x and again plus into minus is minus therefore we have minus 8 t. Hence the product of the second part is x square minus 2 x minus 8 t. So this completes the second part. Now proceeding on to the third part which is 3 x plus 4 into 3 x minus 5. So first let us write down the identity with the help of which we will solve this problem. Suppose we have to multiply y plus a into y plus b and again its formula will be y square plus a plus b into y plus a into b. Now on comparing the left hand side of this identity with the given problem we find that here y is equal to 3 x, a is equal to 4 and b is equal to minus 5. So applying the identity 3 x plus 4 into 3 x minus 5 can be written as first we have y square that is 3 x whole square plus a plus b that is 4 plus minus 5 into y which is 3 x plus a into b that is 4 into minus 5. The 3 x whole square is 9 x square plus 4 plus of minus 5 is minus 1 into 3 x plus 4 into minus 5 is minus 20 which is further equal to 9 x square minus 3 x minus 20. Hence the product of the third part is 9 x square minus 3 x minus 20. So this completes the third part. Now proceeding on to the fourth part which is y square plus 3 upon 2 into y square minus 3 upon 2. Now clear idea was that if we have two binomials x plus a and x plus b then their product is equal to x square plus a plus b into x plus a into b. And on comparing the left hand side of this identity with the given problem we find here that x is equal to y square a is equal to 3 upon 2 and b is equal to minus 3 upon 2. And thus applying the identity y square plus 3 upon 2 into y square minus 3 upon 2 can be written as x square x is y square so y square whole square plus a plus b that is 3 upon 2 plus of minus 3 upon 2 into x which is y square plus a into b that is 3 by 2 into minus 3 upon 2. Now y square whole square is y raised to the power 4 plus 3 by 2 minus 3 by 2 cancels out and we have 0 y square plus on multiplying 3 with minus 3 we get minus 9 and on multiplying 2 with 2 we get 4. So thus we have y raised to the power 4 plus 0 and plus into minus is minus so minus 9 upon 4 which is further equal to y raised to the power 4 minus 9 upon 4 and hence the product of the fourth part is y raised to the power 4 minus 9 upon 4. So this completes the fourth part and let us now proceed on to the last part where we have to find the product of 3 minus 2x and 3 plus 2x. So first let us write down the identity with the help of which we will solve the problem. Suppose we have two binomials y plus a and y plus b and their product is equal to y square plus a plus b into y plus a into b and on comparing the left hand side of this identity with the portion we find here that y is equal to 3, a is equal to minus 2x and b is equal to plus 2x and on applying this identity to 3 minus 2x and 3 plus 2x first we have y square y is 3 so 3 square plus a plus b, a is minus 2x and b is 2x into y so y is 3 plus a into b. So a is minus 2x and b is 2x. Now 3 square is 9 plus minus 2 plus 2x cancels out we have 0 into 3 plus on multiplying minus 2x with plus 2x we have minus 4x square which is equal to 9 plus 0 and plus into minus is minus so minus 4x square which is equal to 9 minus 4x square and hence the product of the last part is 9 minus 4x square. So this completes the last part and hence the solution so hope you enjoyed this session. Take care and have a good day.