How do you find the third term of #(x^2-2)^7#?

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Answer 1 · 2017-02-02T12:03:23

#84x^10.#

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, r=0,1,2,...,n.#

In our Example, we have,

#n=7, r+1=3, or, r=2, a=x^2, and, b=-2#.

Hence, the Reqd. Term #T_3=""_7C_2(x^2)^(7-2)(-2)^2#

#={(7)(6)}/{(1)(2)}(x^2)^5(4)#

#=84x^10.#