A property connecting multiplication and addition, where multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding: a(b + c) = ab + ac.
From Latin 'distributus,' meaning divided or distributed, from 'distribuere' (to divide among). The mathematical concept was formalized as algebra developed, recognizing how multiplication 'distributes' over addition like distributing objects among groups.
The distributive property is the bridge between arithmetic and algebra - it's how we expand expressions and factor polynomials! This property also explains why area works the way it does: a rectangle with width 5 and length (3 + 2) has the same area as two rectangles with widths 5 and lengths 3 and 2 respectively.
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