Explanation

(c)
$\lim_{x \rightarrow 0}\frac{(1 + x)^{8} - 1}{(1 + x)^{2} - 1}$
$= \lim_{x \rightarrow 0}\frac{\left\lbrack (1 + x)^{4} + 1 \right\rbrack\left\lbrack (1 + x)^{2} + 1 \right\rbrack\lbrack(1 + x)^{2} - 1\rbrack}{(1 + x)^{2} - 1}$
$= 2 \times 2 = 4$
Alternate
$\lim_{x \rightarrow 0}\frac{(1 + x)^{8} - 1}{(1 + x)^{2} - 1}\$ $\left( \frac{0}{0}form \right)$
$\ \lim_{x \rightarrow 0}\frac{8(1 + x)^{7}}{2(1 + x)}$ (by L’ Hospital’s rule)
$= 4$