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The algebra properties associated to each case are listed below:Case 1: Distributive propertyCase 3: Associative property (multiplication)Case 5: Existence of inverse (addition)What algebra properties are used in algebraic expressions?In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:Reflexive property of equalities.Symmetric property of equalities.Transitive property of equalities.Compatibility property (addition, multiplication)Commutative property (addition, multiplication).Associative property (addition, multiplication).Existence of inverse (addition, multiplication).Modulative property (addition, multiplication).Distributive property.Now we proceed to determine the property associated to corresponding operation:Case 19 · (x + y) = 9 · x + 9 · y → Distributive propertyCase 3[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)Case 5(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)To learn more on algebra properties: https://brainly.com/question/14523737#SPJ1