What is the expression for the product of 5 and the sum of x and y?

What is the expression for the product of 5 and the sum of x and y?

• A. 5x + y
• B. 5 (x + y)
• C. (5x + 5y)
• D. 5x - y

Answer: (B)

The correct expression for the product of 5 and the sum of x and y can be determined by breaking down the phrase step by step. The phrase "the sum of x and y" refers to the addition of the two variables, which is expressed as \(x + y\). Next, the phrase "the product of 5 and" indicates that this sum should be multiplied by 5. When you combine these two components, you get \(5 \times (x + y)\), which is concisely written as \(5(x + y)\). This clearly shows that 5 is being multiplied by the entire sum of x and y. The other options do not accurately represent this relationship. The first option incorrectly presents the terms as separate products. The third option expands the expression appropriately to show \(5x + 5y\), but it does so under the assumption that the terms were added individually rather than multiplied as a single summed entity. The fourth option indicates a subtraction instead of multiplication, which directly contradicts the original question’s requirements. Thus, the expression \(5(x + y)\) correctly captures the operation as intended.

The correct expression for the product of 5 and the sum of x and y can be determined by breaking down the phrase step by step. The phrase "the sum of x and y" refers to the addition of the two variables, which is expressed as (x + y).

Next, the phrase "the product of 5 and" indicates that this sum should be multiplied by 5. When you combine these two components, you get (5 \times (x + y)), which is concisely written as (5(x + y)). This clearly shows that 5 is being multiplied by the entire sum of x and y.

The other options do not accurately represent this relationship. The first option incorrectly presents the terms as separate products. The third option expands the expression appropriately to show (5x + 5y), but it does so under the assumption that the terms were added individually rather than multiplied as a single summed entity. The fourth option indicates a subtraction instead of multiplication, which directly contradicts the original question’s requirements.

Thus, the expression (5(x + y)) correctly captures the operation as intended.