Final Answer:
The simplified form of the expression −3r(−12r+4r−16) is 24r² + 48r, which corresponds to option D.
Step-by-step explanation:
To simplify the expression, −3r(−12r+4r−16), distribute the −3r across the terms inside the parentheses using the distributive property. Begin by multiplying −3r by each term within the parentheses: −3r * (−12r) + (−3r) * 4r + (−3r) * (−16). This results in 36r² - 12r² + 48r after performing the multiplication.
Upon simplifying further by combining like terms, the expression reduces to 24r² + 48r. Thus, after correctly applying the distributive property and consolidating the terms, the simplified form of −3r(−12r+4r−16) is 24r² + 48r, corresponding to option D.
Therefore, by effectively distributing the −3r across the terms inside the parentheses and subsequently performing the multiplication and addition, the expression simplifies to 24r² + 48r. This demonstrates the correct application of the distributive property and combining like terms to derive the simplified expression.