# Which of the following operations are not distributive? Option 1) Standard Multiplication Option 2) Standard Addition Option 3) $a*b=(a.b)^{2};a+b=\left | a \right |\left | b \right |$ Option 4) All are distributive

H Himanshu

As we learnt

Distributive Binary operation -

a*(b+c)=(a*b)+(a*c)

- wherein

Two binary operation * and + on a set A are functions * : A × A A and +:A x A →A, such that, A × A → A  is said to be distributive, If a*(b+c)=(a*b)+(a*c)

$a*(b+c)=a*(\left | b \right |\left | c \right |)$

$=\left (a.(\left | b \right |\left | c \right |) \right )^{2}$

$= a^{2}b^{2}c^{2}$

$a*b+a*c= \left ( ab \right )^{2}+\left ( ac \right )^{2}= a^{2}b^{2}a^{2}c^{2}= a^{4}b^{2}c^{2}$

Option 1)

Standard Multiplication

Option 2)

$a*b=(a.b)^{2};a+b=\left | a \right |\left | b \right |$