# How to find constant term in binomial theorem

By | 09.04.2021

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Oct 17,  · Let us write the general term of the above binomial. T_(r+1) = "" ^3 C_r (2x)^(3-r) 3^r simplifying, we get, T_(r+1)= "" ^3 C_r 2^(3-r) 3^r x^(3-r) Now for this term to be the constant term, x^(3-r) should be equal to 1. Therefore, x^(3-r)= x^0 => 3-r =0 => r=3 Thus, the fourth term in the expansion is the constant term. May 07,  · About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators.

Example 1 :. Solution :. Constant term :. Example 2 :. Find the last two digits of the number 3 Multiple of 10 ends with 0. By subtracting from multiple of 10, we will get the value ends with 0. Example 3 :. Example 4 :. So, the coefficients of middle terms are equal.

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Binomial Expansions and Pascal’s Triangle

Constant term: 15 - 5r = 0. 15 = 5 r. r = 15/5 = 3 = 5 C 3 (-1/ 3) 3 (2) x 15 - 5(3) = (/27) ? 4 = / So, the constant term is / Example 2: Find the last two digits of the number 3 Solution: 3 = (3 2) = (9) = (10 - 1) If you want to do it using strictly BINOMIAL THEOREM, you can do it as follows: (x + 1 x + 1)7 = ((x + 1 x) + 1)7 = 1 + (7 1)(x + 1 x) + (7 2)(x + 1 x)2 + + (7 7)(x + 1 x)7 Now in the expansion of (x + 1 x)n, the constant term is: Tr + 1 = (n r)x2r ? n = (n r) 2 | n. How To: Given a binomial, write a specific term without fully expanding. Determine the value of $n$ according to the exponent. Determine $\left(r+1\right)$. Determine $r$. Replace $r$ in the formula for the $\left(r+1\right)\text{th}$ term of the binomial expansion.

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