 Hello and welcome to the session. Here we will discuss the following question which says that expand 4-3x whole raise to power minus 5 as far as the term containing x raise to power 3 also mention the condition for the validity of the expansion. Now before starting the solution of this question we all should know the expansion of the binomial expression and that is 1 plus x raise to power n is equal to 1 plus nx plus n into n minus 1 over 1 into 2 into x square plus n into n minus 1 into n minus 2 over 1 into 2 into 3 into x cube plus so on up to infinity. There the absolute value of x is less than 1 and n be any negative integer. So this result will work out as a key idea for solving out this question and now we will start with the solution. Here we have to expand 4 minus 3x whole raise to power minus 5. Now before expanding this we have to make the first term equal to unity. So this will be equal to 4 raise to power minus 5 inside 1 minus 3 by 4x whole raise to power minus 5. Now by using the expansion which is given in the key idea here x is minus 3 by 4x and n is minus 5. Now using the expansion this will be equal to 4 raise to power minus 5 inside 1 plus minus 5 into minus 3 by 4x plus minus 5 into minus 5 minus 1 over 1 into 2 into minus 3 by 4x whole square plus minus 5 into minus 5 minus 1 into minus 5 minus 2 over 1 into 2 into 3 into minus 3 by 4x whole cube plus so on. So we are getting 1 plus nx plus n into n minus 1 over 1 into 2 into x square plus n into n minus 1 into n minus 2 over 1 into 2 into 3 into x cube. Here n is minus 5 and x is minus 3 by 4x. Further this will be equal to 1 over 4 raise to power 5 inside 1 plus minus 5 into minus 3 is 15 by 4x plus minus 5 minus 5 minus 1 is minus 6 over 1 into 2 is 2 into minus 3 by 4x square will give 9 by 16 x square plus minus 5 into minus 5 minus 1 is minus 6 minus 5 minus 2 is minus 7 over 1 into 2 into 3 is 6 into minus 3 by 4 x cube will be minus 27 by 64 x cube plus so on. Further this will be equal to 1 over 4 raise to power 5 inside 1 plus 15 by 4x plus here 2 into 3 is 6 so it will be minus 5 into minus 3 into 9 by 16 x square plus here 6 will be cancelled with 6. So it will be minus 5 into minus 1 into minus 7 into minus 27 by 64 x cube plus so on. So this will be equal to 1 over 4 raise to power 5 into 1 plus 15 by 4x plus here minus 5 into minus 3 into 9 is 6. This will give 135 over 16 x square plus here minus 5 into minus 1 into minus 7 into minus 27 will give 945 over 64 x cube plus so on. So this is the expansion of 4 minus 3x whole raise to power minus 5 up to the term containing x raise to power 3. Now we have to mention the condition for the validity of expansion. The expansion is valid only when absolute value of minus 3 by 4x is less than 1. That is when absolute value of 3 by 4x is less than 1. That is when absolute value of x is less than 4 by 3. That is when the value of x lies between minus 4 by 3 and 4 by 3. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.