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QUESTION

# How do I use the binomial theorem to find the constant term?

Let (2x+3) ^3 be a given binomial.

From the binomial expression, write down the general term. Let this term be the r+1 th term. Now simplify this general term. If this general term is a constant term, then it should not contain the variable x. 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. By putting r=3 in the general term, we will get the value of the constant term.