# Distributive Property

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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.