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 $T_3=""_7C_2(x^2)^(7-2)(-2)^2$

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

$=84x^10.$

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