Integers and Rational Numbers Distributive property: Whole number coefficients Español Use the distributive property to remove the parentheses. \[ 4(v-3) \] \( \square \) Explanation Check © 2025 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Accessibility

To use the distributive property to remove the parentheses in the expression \(4(v-3)\), we follow these steps: 1. **Identify the components**: The expression consists of a coefficient \(4\) and a binomial \(v - 3\). 2. **Apply the distributive property**: The distributive property states that \(a(b + c) = ab + ac\). In this case, we can apply it as follows: \[ 4(v - 3) = 4 \cdot v + 4 \cdot (-3) \] 3. **Perform the multiplication**: - For the first term: \(4 \cdot v = 4v\) - For the second term: \(4 \cdot (-3) = -12\) 4. **Combine the results**: Now we can write the expression without parentheses: \[ 4(v - 3) = 4v - 12 \] Thus, the final answer is: \[ 4v - 12 \] ### Explanation The distributive property allows us to multiply a single term by each term inside a set of parentheses. In this case, we multiplied \(4\) by both \(v\) and \(-3\) to eliminate the parentheses. ### Check To verify, we can substitute a value for \(v\) and check if both forms of the expression yield the same result. For example, if \(v = 5\): - Original expression: \(4(5 - 3) = 4(2) = 8\) - Simplified expression: \(4 \cdot 5 - 12 = 20 - 12 = 8\) Both expressions yield the same result, confirming that our application of the distributive property is correct.