The most important part of slimming down is diet control.
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usage
瘦身 emphasizes aesthetic slimming and reshaping; 减肥 (jiǎnféi) is the broader everyday term for losing weight. Advertising tends to prefer 瘦身 because it sounds softer and more lifestyle-oriented.
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Also used metaphorically in business Chinese for a company trimming staff, costs, or product lines — the Taiwan usage has spread to the mainland.