What mathematical property is illustrated by a(b + c) = ab + ac?

What mathematical property is illustrated by a(b + c) = ab + ac?

• A. Commutative property
• B. Associative property
• C. Additive property
• D. Distributive property

Answer: (D)

The equation a(b + c) = ab + ac demonstrates the distributive property. This property states that when a number is multiplied by a sum, it is equivalent to multiplying each addend in the sum individually by that number and then adding the results. In this case, the term 'a' is distributed to both 'b' and 'c', showing how the multiplication interacts with addition. This principle is essential for simplifying expressions and solving equations in algebra. It helps students understand how operations can be applied in various ways while maintaining equivalence, which is a foundational concept in mathematics. It plays a critical role in computations ranging from basic arithmetic to more complex algebraic manipulations. Other mathematical properties, such as the commutative and associative properties, relate to the order and grouping of numbers but do not apply in this situation. The additive property generally addresses the behavior of addition, which is also not relevant here. Thus, the distributive property is the key concept exemplified in the given equation.

The equation a(b + c) = ab + ac demonstrates the distributive property. This property states that when a number is multiplied by a sum, it is equivalent to multiplying each addend in the sum individually by that number and then adding the results. In this case, the term 'a' is distributed to both 'b' and 'c', showing how the multiplication interacts with addition.

This principle is essential for simplifying expressions and solving equations in algebra. It helps students understand how operations can be applied in various ways while maintaining equivalence, which is a foundational concept in mathematics. It plays a critical role in computations ranging from basic arithmetic to more complex algebraic manipulations.

Other mathematical properties, such as the commutative and associative properties, relate to the order and grouping of numbers but do not apply in this situation. The additive property generally addresses the behavior of addition, which is also not relevant here. Thus, the distributive property is the key concept exemplified in the given equation.