Distributive Property

Distributive Property Distributive property is a well known property of binary operations that basically deals with the distributive law. This property can be explained by taking three variables x, y and z. This can be represented as follows: - x* (y + z) = x*y + x*z This can be more clarified by taking suitable examples. Problem 1: Evaluate the following by the use of distributive property a) 2 * ( 3 + 5) b)4* ( 6 + 5) c)3* (10 + 10) Solution: (a) Given 2* (3+5) = By applying Distributive property that is x* (y + z) = x*y + x*z = Therefore 2* (3+5) = 2*3 + 2*5 = 6 + 10 = 16 (b) Given 4* (6+5) = By applying Distributive property that is x* (y + z) = x*y + x*z = Therefore 2* (3+5) = 4*6 + 4*5 = 24 + 20 = 44 (c) Given 3* (10 + 10 ) = By applying Distributive property that is x* (y + z) = x*y + x*z = Therefore 3* (10 + 10) = 3 * 10 + 3* 10 = 30 + 30 = 60. Problem 2: Solve i (i+ i). Here i is iota of complex number. Solution: Given i (i+ i) = By applying Distributive property that is x* (y + z) = x*y + x*z = Therefore, i * (i+ i) = i*i + i*i = i^2 + i^2 = -1 + (-1) ( Because value of i^2 = -1) = -2.