Final answer:
Promoting the expansion of industry does not represent a way in which William Jennings Bryan appealed to Populists; his campaign was focused on agricultural interests and monetary reform rather than pro-business policies like those of his opponent.
Step-by-step explanation:
The question asks which option does not represent how William Jennings Bryan appealed to the Populists. Among the options - attacking the gold standard, supporting free silver, advocating for farmers' rights, and promoting the expansion of industry - the latter does not align with Bryan's appeals to the Populist movement. While Bryan did come from a farm background, supported free silver, and advocated for farmers' rights, he did not promote the expansion of industry, which was more aligned with his opponent William McKinley's platform. McKinley's campaign resonated with governors, bankers, and was focused on the gold standard and maintaining current economic policies, whereas Bryan's campaign was largely focusing on the interests of the Populists, which included a silver standard to help alleviate the economic burdens on farmers.