 Hello and welcome to the session. I am Arsha and I am going to help you to solve the following question that says find the expansion of 3x square minus 2x plus 3a square raised to the power 3 using binomial theorem. So, let us begin with the solution and we have to expect 3x square minus 2ax plus 3a square raised to the power 3 which can further be written as 3x square minus a into 2x minus 3a raised to the power 3 and now we are applying the binomial theorem which is 3c0 3x square raised to the power 3 into minus a into 2x minus 3a raised to the power 0 plus 3c1 3x square raised to the power 2 into minus a into 2x minus 3a raised to the power 1 plus 3c2 3x square raised to the power 1 into minus a into 2x minus 3a whole square 3c3 3x square raised to the power 0 into minus a into 2x minus 3a raised to the power 3. So, this is further equal to 3c0 as 1 and 3 whole cube into x square cube and minus a into 2x minus 3a whole raised to the power 0 as 1 plus 3c1 as 3 into 3 square into x square whole square and then we have minus 2ax plus 3a square plus 3c2 as again 3 into 3x square and we have minus 2ax plus 3a square whole square plus 3c3 as 1 and 3x square raised to the power 0 is again 1 and inside the bracket we have minus 2ax plus 3a square raised to the power 3 which is further equal to 27x raised to the power 6 plus 27x raised to the power 4 into minus 2ax plus 3a square plus 9x square into minus 2ax plus 3a square whole square plus minus 2ax plus 3a square whole cube which is further equal to 27x raised to the power 6 plus 27x raised to the power 4 into a minus 2x plus 3a now plus 9x square into minus 2ax whole square plus 3a square whole square plus 2 times of minus 2ax into 3a square plus now applying the formula of u plus 3 whole cube here we have minus 2ax whole cube plus 3 into minus 2ax into 3a square whole square plus 3 times of minus 2ax whole square into 3a square plus 3a square whole cube this is further equal to 27x raised to the power 6 minus 54x raised to the power 5 into a plus 81x raised to the power 4 into a square plus 9x square now simplifying the curly bracket we have 4a square x square plus 9a raised to the power 4 plus into minus is minus so we have 2 to the power 4 4 3s are 12a cube into x plus now simplifying the next curly bracket we have minus 2ax whole cube so this is 8 with a negative sign a cube x cube and here we have 3 3s and 9 and 3s are 27 and 27 into minus 2s and is 54 a raised to the power 5 into x plus 2 to the power 4 4 3s are 12 and 12 3s are 36 a raised to the power 4 x square plus 27 a raised to the power 6 which is further equal to 27 x raised to the power 6 minus 54 x raised to the power 5 into a and here on simplifying it further we have plus 1 a d 1 x raised to the power 4 into a square plus 9 4s are 36 a square x raised to the power 4 plus 9 9s a d 1 x square a raised to the power 4 and multiplying 9 with minus 12 minus 108 a cube x cube minus 8 a cube x cube minus 54 a raised to the power 5 into x plus 36 a raised to the power 4 into x square plus 27 a raised to the power 6 now collecting the light terms and simplifying them we have 27 x raised to the power 6 minus 54 x raised to the power 5 into a now a square x raised to the power 4 this term a square x raised to the power 4 we have one more term of this letter and and and simplifying on these two we have plus 117 x 4 a square now let us simplify the terms having the literal a cube x cube so I am simplifying these two we have minus 116 a cube x cube now simplifying the terms having the literal a raised to the power 4 into x square so we have these two terms on an adding we get plus 117 a raised to the power 4 into x square now simplifying a raised to the power 5 into x there is only one term having this little so we have minus 54 a raised to the power 5 into x plus and lastly we have 27 a raised to the power 6 hence our answer is 27 x raised to the power 6 minus 54 a into x raised to the power 5 plus 117 a square x raised to the power 4 minus 116 a cube x cube plus 117 a 4 x square minus 54 a raised to the power 5 into x plus 27 a raised to the power 6 this is the expansion and this completes the solution take care and bye for now