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00:00 - 00:59 | in this question we are required to find the middle term in the expansion of X + 2 raise to 6 now for such expansions if the value of x + 2 raise to N suppose we are for the time being we are not considering the sticks if the value of n is even then the middle term is given by and by 2 + 1 or 2 term and if any equals to odd if n is odd number then we have two middle terms two middle terms which are given by N + 1 by 2 Earth term and and by 2 + 18 these Aadha this is the proper convention no in this case X + 2 raise to 6 we have |

01:00 - 01:59 | and to be even that mean middle term would be and by 2 + 18 term or 6 by 2 + 1 earth which will give me this is 33 plus one that meets fourth down so we are only required to find out the 4th term now I can write the general term for this expression general Thomas t r + 1 = 2 NCR X raise to n minus are and tourist to required to find the 4th term that means T4 in this case are plus one in the form of h + 1 I can write this as three plus one that means the value of Rs 3 not putting here the values of N N are so this will be 63 X |

02:00 - 02:59 | raise to 6 -3 tourist 3 now solving this the value of this combination will be 6 factorial 6 - 3 factorial into 3 factorial in x cube into 8 for the solving this text into 5 into 4 into 3 factorial divided by 6 - 33 only and this 3 factorial not this will be cancelled by this into it is also there in the next step 6 into 5 into 4 into a divided by 3 factorial is 3 into 2 into 1 that means 6210 24 31 32 and the final don't forget x cube is also there we are required to find out the whole term not only the coefficient so this will be to |

03:00 - 03:59 | into 5 into 4 into 4 into x cube this will be 10 into this will be 16 X cube to the term finally is coming out to be 160 x cube this is the middle term that you are required to find out in question thank you |

**Introduction**

**State & proof Binomial Theorem and Pascal triangle**

**Number of terms in expansion of following
(i) `(2x-3y)^9` (ii) `(2x+3y-4z)^n`**

**Expand `(x^2+2a)^5`; `(2x-3y)^4`;`(1+x+x^2)^3` by binomial theorem**

**(iii) Find an approximate value of `(0.99)^5` using the first three terms of its expansion.**

**Using binomial theorem prove that `(101)^50 gt(100)^50+(99)^50`**

**What is General and middle term in a binomial expansion**

**Term from the end of expansion**

**Coefficient of certain power of variable in binomial**

**finding term independent of variable**