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Rule

Zero Property of Multiplication

The result of multiplying any number by  is always
As a consequence of this, if an entire expression is multiplied by the result is It does not matter the number of terms that the expression has.

Proof

Consider a number multiplied by zero.
The number zero can be rewritten as the subtraction of any number from itself. For simplicity, the zero can be rewritten as
Then the number can be distributed to simplify the expression on the right-hand side of the equation.
It has been shown that By the Commutative Property of Multiplication, is also equal to