Final answer:
The expression 2(3+4) can be rewritten using the distributive property as 2(3) + 2(4), which simplifies to 6 + 8, and those terms can be combined to result in 14. No other property or operation needs to be applied once the terms have been combined correctly.
Step-by-step explanation:
The student has asked to rewrite the expression 2(3+4) into two equivalent expressions and to identify the properties utilized to rewrite them. First, using the distributive property, we can expand the expression to 2(3) + 2(4), which shows that each term within the parentheses is multiplied by the number outside the parentheses. Secondly, we can simplify the expression 6 + 8 by evaluating the multiplication of each term, which uses the property that when two positive numbers multiply, the answer has a positive sign, as in 2x3 = 6 and 2x4 = 8.
To finish, by adding the results together, we get 14. Here, we have used the property of combining like terms which simply adds together numbers that are not attached to variables. It is crucial to note that options b) and d) in the question are incorrectly written, as b) does not represent an accurate step, and d) is a final computed value rather than a property. Referencing the provided information on multiplication rules for signs and the correct way to combine terms helps ensure each step taken to simplify the expression is valid and can be checked for reasonableness.