Final Answer:
The distributive property was employed in Step 3 of the problem's simplification process, wherein a value outside the parentheses was multiplied by each term inside, expanding the expression accordingly. This step exemplifies the application of the distributive property in simplifying mathematical expressions. Thus, the correct answer is option 3.
Explanation:
The distributive property in mathematics is utilized when we need to multiply a value by the sum or difference of two or more terms within parentheses. It involves distributing the value to each term inside the parentheses. For instance, if we have an expression like a × (b + c), the distributive property dictates that we multiply 'a' by both 'b' and 'c' individually, resulting in a × b + a × c.
In the context of the problem steps provided, let's consider a hypothetical expression simplification, say 3 × (2 + 4). If this expression is being simplified step by step, in Step 1, one might perform the addition within the parentheses resulting in 3 × 6. Step 2 could involve multiplying 3 by 6, yielding 18. However, if in Step 3, there's a step where the number 3 is distributed to both terms inside parentheses (e.g., 3 × 2 + 3 × 4), this aligns with the application of the distributive property.
Identifying the step in which the distributive property is used involves recognizing when a value outside the parentheses is multiplied by each term inside the parentheses, resulting in the expansion of the expression. Therefore, Step 3 would be the appropriate step in which the distributive property was applied to simplify the problem (option 3).
Question:
In a sequence of steps aimed at simplifying a mathematical problem, the distributive property was utilized in Step 3. This involved multiplying a value outside the parentheses by each term inside, thereby expanding the expression. How does this specific step demonstrate the application and significance of the distributive property in the process of simplifying mathematical expressions?