 Hello and welcome to the session. Today I will help you with the following question. The question says simplify A plus B multiplied with C minus D plus A minus B multiplied with C plus D plus 2 times AC plus BD. Now the distributive law of multiplication is A multiplied by B plus C is equal to A multiplied by B plus A multiplied by C. Also commutative law is A multiplied by B is equal to B multiplied by A. Now this is taken as the key idea in this question. Now let's move on to the solution. The expression given to us is A plus B multiplied with C minus D plus A minus B multiplied with C plus D plus 2 times AC plus BD. Now first we will find the value of this expression that is A plus B multiplied with C minus D. Now using the distributive law of multiplication we have A plus B multiplied with C plus A plus B multiplied with minus D. Now with the help of commutative law we get C multiplied by A plus B plus minus D multiplied by A plus B. Now again we will apply the distributive law of multiplication and so this is equal to C multiplied by A plus C multiplied by B plus minus D multiplied by A plus minus D multiplied by B. And this is equal to AC plus BC minus AD minus BD. Hence we have A plus B multiplied by C minus D is equal to AC plus BC minus AD minus BD. Now next we will find the value of the expression A minus B multiplied by C plus D. That is A minus B multiplied by C plus D. Now we will use the distributive law of multiplication so we get A minus B multiplied with C plus A minus B multiplied with D. And now we will use the commutative law so we have C multiplied by A minus B plus D multiplied by A minus B. Now again we will use the distributive law of multiplication. Now using that we get C multiplied by A plus C multiplied by minus B plus D multiplied by A plus D multiplied by minus B. And so this further is equal to AC minus BC plus AD minus BD. And so we say that A minus B multiplied with C plus D is equal to AC minus BC plus AD minus BD. And now we shall find the value of this expression. The expression is 2 multiplied by AC plus BD. Now using the distributive law of multiplication we have 2 multiplied by AC plus 2 multiplied by BD. And this is further equal to 2 AC plus 2 BD. Thus we have got 2 multiplied by AC plus BD is equal to 2 AC plus 2 BD. So we have the given expression is equal to AC plus BC minus AD minus BD plus AC minus BC plus AD minus BD plus 2 AC plus 2 BD. Now we will combine the like terms. So we have AC plus AC plus 2 AC then we have plus BC minus BC and then we have plus AD minus AD. And then plus 2 BD minus BD and one more minus BD. Now here plus BC minus BC gets cancelled plus AD minus AD gets cancelled 2 BD minus BD minus BD. All the 3 terms gets cancelled to each other. So we are left with AC plus AC plus 2 AC and that is equal to 4 AC. And hence our given expression is simplified to 4 AC and so our final answer is 4 AC. So hope you enjoyed the session. Have a good day.