# How to find constant term in binomial theorem

By | 09.04.2021

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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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