 Hello and welcome to the session. In this session we discussed the following question that says, what must be added to 2x square minus 2x minus 3 to make the sum 6xq minus x square plus 3x plus 1. Let's move on to the solution now. The sum of the 2 expressions or 2 algebraic expressions is given as xq minus x square plus 3x plus 1. We are given 1 algebraic expression x square minus 2x minus 3. To find the second algebraic expression, we subtract the first algebraic expression from the sum that is 6xq minus x square plus 3x plus 1 minus 2x square minus 2x minus 3. Now we write these expressions column wise by writing the light terms in one column. So we have this is equal to 6xq minus x square plus 3x plus 1. Now the second expression that is 2x square minus 2x minus 3 and we write it below this expression in such a way that the light terms are in a column. So it would be 2x square minus 2x minus 3. Now as we need to subtract, so we will change the sign of the second expression. So this would be minus this would be plus and this would be plus again. And so this is equal to 6xq would be written as it is. Then we have minus x square minus 2x square. So it becomes minus 3x square. Then 3x plus 2x becomes plus 5x. Then 1 plus 3 becomes plus 4. So thus we can now say that 6xq minus 3x square plus 5x plus 4 must be added to x square minus 2x minus 3 to get the sum as 6xq minus x square plus 3x plus 1. This is our final answer. This completes the session. Hope you have understood the solution of this question.