What does the distributive property express mathematically?

What does the distributive property express mathematically?

• A. (a + b) × c = a × c + b × c
• B. a(b + c) = ab + ac
• C. a(b - c) = ab - ac
• D. (a - b) + c = a - (b + c)

Answer: (B)

The distributive property is a fundamental concept in mathematics that describes how multiplication interacts with addition or subtraction. It expresses that multiplying a single term by a sum or difference can be distributed to each term within that operation. The choice indicating a(b + c) = ab + ac accurately reflects this property. Here, when 'a' is multiplied by the sum of 'b' and 'c', it effectively means that 'a' is multiplied by 'b' and also by 'c', and then those results are added together. This showcases the distributive nature of multiplication over addition. Understanding how this property works is crucial for simplifying expressions and solving equations. It allows for breaking down complex problems into simpler parts, making it easier to work with numbers and variables.

The distributive property is a fundamental concept in mathematics that describes how multiplication interacts with addition or subtraction. It expresses that multiplying a single term by a sum or difference can be distributed to each term within that operation.

The choice indicating a(b + c) = ab + ac accurately reflects this property. Here, when 'a' is multiplied by the sum of 'b' and 'c', it effectively means that 'a' is multiplied by 'b' and also by 'c', and then those results are added together. This showcases the distributive nature of multiplication over addition.

Understanding how this property works is crucial for simplifying expressions and solving equations. It allows for breaking down complex problems into simpler parts, making it easier to work with numbers and variables.