Answer: All soaps are long chain fatty acids, but not all soaps have inseciticidal properties. Insecticidal soaps are specifically formulated to have high insect-killing properties, while being safe for most plants.
Insecticidal soaps kill susceptible insects by washing away the protective coating on the surface of the insect and by disrupting normal membrane functions inside the insect. The insects must come into direct contact with the spray droplets for the material to be effective. Good coverage is essential. The soaps have no residual activity toward insects, but repeated applications may have damaging effects on some types of plants.
There are many brandnames available; "Safer's Insecticidal Soap" is an example of one you might find on the shelves of a local garden shop.
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