Algebra laws
1. Commutative Property of Addition. a + b = b + a Examples: 1. real numbers 2 + 3 = 3 + 2 2. algebraic expressions x 2 + x = x + x 2 2. Commutative Property of Multiplication. a × b = b × a Examples: 1. real numbers 5 × 7 = 7 × 5 2. algebraic expressions (x 3 - 2) × x = x × (x 3 - 2) 3. Associative Property of Addition. (a + b) + c = a + (b + c) Examples: 1. real numbers (2 + 3) + 6 = 2 + (3 + 6) 2. algebraic expressions (x 3 + 2 x) + x = x 3 + (2 x + x) 4. Associative Property of Multiplication. (a × b) × c = a × (b × c) Examples: 1. real numbers (7 × 3) × 10 = 7 × (3 × 10) 2. algebraic expressions (x 2 × 5 x) × x = x 2 × (5 x × x) 5. Distributive Properties of Addition Over Multiplication. a × (b + c) = a × b + a × c and (a + b) × c = a × c + b × c Examples: 1. real numbers 2 × (2 + 8) = 2 × 2 + 2 × 8 (2 + 8) × 10 = 2 × 10 + 8 × 10 2. algebraic expressions x × (x 4 + x) = x × x 4 + x × x (x 4 + x) × x 2 = x 4 × x 2 + x × x 2 6. The reciprocal of a non zero real number a is 1/a. an...