When using the distributive property, what is the correct form of the expression a(b+c)?

When using the distributive property, what is the correct form of the expression a(b+c)?

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

Answer: (A)

The expression a(b+c) demonstrates the distributive property, which states that when a single term is multiplied by a sum, it can be distributed to each term in the sum. In this case, you have a multiplying the sum of b and c. Applying the distributive property means you multiply a by each individual term inside the parentheses separately. So, you take a times b, which gives you ab, and then take a times c, which results in ac. When you combine these results, you get the correct expression as (ab) + (ac). This clarification reinforces why the other options do not represent the correct application of the distributive property. They either alter the terms or the operations, which does not correctly express the initial multiplication of a with the sum of b and c.

The expression a(b+c) demonstrates the distributive property, which states that when a single term is multiplied by a sum, it can be distributed to each term in the sum. In this case, you have a multiplying the sum of b and c.

Applying the distributive property means you multiply a by each individual term inside the parentheses separately. So, you take a times b, which gives you ab, and then take a times c, which results in ac. When you combine these results, you get the correct expression as (ab) + (ac).

This clarification reinforces why the other options do not represent the correct application of the distributive property. They either alter the terms or the operations, which does not correctly express the initial multiplication of a with the sum of b and c.