 Hello and welcome to the session. In this session we will discuss a question which says that write the difference of the given polynomials for x square minus 3x minus 7 the whole minus of 5 minus 3x plus 8x square the whole and second part is subtract minus 2x cube plus x square minus 6x plus 10 from 1 into x is to power 4 minus 10x cube plus 13x minus 11. Now let us start with the solution of the given question. Now in the first part we have to write 4x square minus 3x minus 7 the whole minus of 5 minus 3x plus 8x square the whole. First of all we will open the brackets and we get 4x square minus 3x minus 7 minus 5 minus of minus 3x will be plus 3x and minus of plus 8x square will be minus 8x square. Now since the commutative and associative properties hold in polynomials so we can integrate the position of terms so here combining the light terms we get now here we can see that 4x square and minus 8x square are light terms similarly minus 3x and plus 3x are light terms and here minus 7 and minus 5 are light terms. So here we get 4x square minus 8x square the whole plus of minus 3x plus 3x the whole plus of minus 7 minus 5 the whole. Now this is equal to now 4x square minus 8x square is minus 4x square plus now minus 3x plus 3x is 0 plus here minus 4x square minus 5 is minus 12 so this is equal to minus 4x square plus 0 plus of minus 12 which is equal to minus 4x square minus 12. Simplifying the first part we obtain minus 4x square minus 12. Now let us start with the second part. For the second part we have to subtract minus 2x cube plus 4x square minus 6x plus 10 from 4 into x raise to power 4 minus 10x cube plus 13x minus 11. It means we have to find 4 into x raise to power 4 minus 10x cube plus 13x minus 11 the whole minus of minus 2x cube plus 4x square minus 6x plus 10 the whole. Now we will open the brackets and this is equal to 4 into x raise to power 4 minus 10x cube plus 13x minus 11 plus 2x cube minus 4x square plus 6x minus 10. And now we will combine the like terms. Now where you can see minus 10x cube plus 2x cube are like terms then 13x minus 11 and minus 10 are like terms. This is equal to 4 into x raise to power 4 plus of minus 10x cube plus 2x cube the whole minus 4x square plus 6x the whole plus of minus plus x cube minus 4x. 13x plus 6x plus 19x 7 minus 10 that is minus 21. Now this is equal to raise to power 4 minus 4x square plus 19x minus 21 and this completes our session hope you all have enjoyed this session.