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# 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.