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Rule

Zero Property of Multiplication

The result of multiplying any number by 0 is always 0.

a*0=0

As a consequence of this, if an entire expression is multiplied by 0, the result is 0. It does not matter the number of terms that the expression has. (a+29-3b+12* xy0.24)*0=0 endgathered

Proof

Consider a number a multiplied by zero. a* 0 The number zero can be rewritten as the subtraction of any number from itself. For simplicity, the zero can be rewritten as 1-1. a* 0 = a* (1-1) Then the number a can be distributed to simplify the expression on the right-hand side of the equation.

a* 0 = a* (1-1)

Distr

Distribute a

a* 0 = a-a

DiffZero

a-a=0

a*0 = 0

It has been shown that a*0=0. By the Commutative Property of Multiplication, 0* a is also equal to 0.

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