How do you find the fourth term of #(x+2)^7#?

1 Answer
Jan 11, 2017

Answer:

#280x^4#

Explanation:

Recall that the #(r+1)^(th)# term #T_(r+1)# in the expansion of

#(a+b)^n# is given by, #T_(r+1)=""_nC_ra^(n-r)b^r#.

In our Example, we have,

#n=7, a=x, b=2, &, r+1=4, i.e., r=3#

#:. T_(3+1)=T_4=""_7C_3(x^(7-3))(2^3)=(7.6.5)/(1.2.3)(x^4)8#

Hence, the reqd. term #T_4=280x^4#.

Alternatively, we can expand #(x+2)^7# using the Binomial

Theorem ** upto the reqd. #4^(th)# term, as shown below :

#(x+2)^7=""_7C_0(x^(7-0))(2^0)+""_7C_1(x^(7-1))(2^1)+""_7C_2(x^(7-2))(2^2)+""_7C_3(x^(7-3))(2^3)+...+"Last Term"#, giving the same Answer.