What property is illustrated by the equation 4(x + 3) = 4x + 12?

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The equation 4(x + 3) = 4x + 12 demonstrates the Distributive Property. This property states that when you multiply a number by a sum, you can distribute the multiplication across each term in the sum.

In the equation, 4 is multiplied by the entire expression (x + 3). According to the Distributive Property, this can be accomplished by multiplying 4 by each term inside the parentheses separately: 4 multiplied by x gives 4x, and 4 multiplied by 3 gives 12. Thus, the expression expands to 4x + 12. The ability to do this transformation is what characterizes the Distributive Property.

In contrast, the other properties listed do not apply here. The Commutative Property pertains to changing the order of operands in operations like addition or multiplication, while the Associative Property involves changing the grouping of operands. The Identity Property relates to the concept that adding zero or multiplying by one leaves a number unchanged. None of these properties are relevant in the context of this equation.

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