According to the distributive property, how can the expression a(b + c) be expanded?

• A. ab + bc
• B. ab + ac
• C. (ab)c
• D. a + b + c

Answer: (B)

The expression a(b + c) can be expanded using the distributive property, which states that when you have a term multiplied by a sum, you can distribute the multiplication to each term in the sum.

In this case, 'a' is multiplied by the entire sum of 'b' and 'c'. Therefore, you would take 'a' and multiply it by 'b', resulting in 'ab', and then take 'a' and multiply it by 'c', resulting in 'ac'. This gives us the full expanded form of the original expression, which is ab + ac.

This understanding reflects how the distributive property works in algebra by allowing the multiplication to be applied to each component within the parentheses individually, ensuring that the relationships between the terms are maintained while simplifying the expression.