How do you find the constant term in a binomial expansion?
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Let(2x+3) ^3be a given binomial.
From the binomial expression, write down thegeneral term. Let this term be ther+1th 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_r2^(3-r)3^rx^(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. hope help y
Let(2x+3) ^3be a given binomial.
From the binomial expression, write down thegeneral term. Let this term be ther+1th 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_r2^(3-r)3^rx^(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. hope help y
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