Which principle is represented by a(b + c) = ab + ac?

Which principle is represented by a(b + c) = ab + ac?

• A. Distributive Property
• B. Commutative Property
• C. Associative Property
• D. Simplification Rule

Answer: (A)

The principle represented by the expression a(b + c) = ab + ac is known as the Distributive Property. This property demonstrates how multiplication distributes over addition. Essentially, it illustrates that when a number (a) is multiplied by the sum of two other numbers (b and c), the result equals the sum of the products of a multiplied by each of those two numbers individually. This principle is foundational in algebra and is extensively used in simplifying expressions and solving equations. The other properties mentioned do not apply to this situation. For instance, the Commutative Property refers to the ability to change the order of addition or multiplication without affecting the outcome (for example, a + b = b + a or ab = ba), while the Associative Property deals with how numbers are grouped in addition or multiplication (for example, (a + b) + c = a + (b + c)). Lastly, the Simplification Rule usually pertains to reducing expressions to simpler forms rather than manipulating the structural relationships of numbers as seen in the Distributive Property. Therefore, the correct answer is indeed the Distributive Property.

The principle represented by the expression a(b + c) = ab + ac is known as the Distributive Property. This property demonstrates how multiplication distributes over addition. Essentially, it illustrates that when a number (a) is multiplied by the sum of two other numbers (b and c), the result equals the sum of the products of a multiplied by each of those two numbers individually. This principle is foundational in algebra and is extensively used in simplifying expressions and solving equations.

The other properties mentioned do not apply to this situation. For instance, the Commutative Property refers to the ability to change the order of addition or multiplication without affecting the outcome (for example, a + b = b + a or ab = ba), while the Associative Property deals with how numbers are grouped in addition or multiplication (for example, (a + b) + c = a + (b + c)). Lastly, the Simplification Rule usually pertains to reducing expressions to simpler forms rather than manipulating the structural relationships of numbers as seen in the Distributive Property. Therefore, the correct answer is indeed the Distributive Property.