Chapter 11 - Sequences; Induction; the Binomial Theorem - Chapter Review - Review Exercises - Page 859: 33

$84$

According to the Binomial Theorem, the term containing $x^j$ in the expansion of $(ax+b)^n$ can be expressed as: $(ax+b)^n =\dbinom{n}{n-j} a^{j}b^{n-j} x^j$ We know that $\dbinom{n}{m}=\dfrac{n!}{(n-m)! \ m!}$. We have: $a=2$ and $n=7$ Thus, the coefficient of $x^2$ is equal to: $ \dbinom{7}{7-2} \ 2^2 \ (1) ^{(7-2)}= \dfrac{7! }{5 ! \ 2 !} \times 4 =84$