Which property states that a(b + c) = (a × b) + (a × c)?

Which property states that a(b + c) = (a × b) + (a × c)?

• A. Associative Property
• B. Distributive Property
• C. Commutative Property
• D. Identity Property

Answer: (B)

The property that states \( a(b + c) = (a \times b) + (a \times c) \) is known as the Distributive Property. This property allows us to distribute a single term outside of parentheses to each term inside the parentheses, effectively breaking it down into a sum of products. For example, if you have to calculate \( 3(4 + 5) \), using the Distributive Property, you can rewrite it as \( (3 \times 4) + (3 \times 5) \), which simplifies the calculation of \( 12 + 15 = 27 \). This property is fundamental in algebra as it helps in simplifying expressions and solving equations that involve addition and multiplication. In contrast, the Associative Property pertains to how numbers are grouped in addition or multiplication without changing the result, while the Commutative Property relates to changing the order of numbers in addition or multiplication. The Identity Property refers to the concept that adding zero to a number or multiplying by one does not change the number. These properties serve different purposes in mathematics, making the Distributive Property unique in how it connects addition and multiplication operations.

The property that states ( a(b + c) = (a \times b) + (a \times c) ) is known as the Distributive Property. This property allows us to distribute a single term outside of parentheses to each term inside the parentheses, effectively breaking it down into a sum of products.

For example, if you have to calculate ( 3(4 + 5) ), using the Distributive Property, you can rewrite it as ( (3 \times 4) + (3 \times 5) ), which simplifies the calculation of ( 12 + 15 = 27 ). This property is fundamental in algebra as it helps in simplifying expressions and solving equations that involve addition and multiplication.

In contrast, the Associative Property pertains to how numbers are grouped in addition or multiplication without changing the result, while the Commutative Property relates to changing the order of numbers in addition or multiplication. The Identity Property refers to the concept that adding zero to a number or multiplying by one does not change the number. These properties serve different purposes in mathematics, making the Distributive Property unique in how it connects addition and multiplication operations.