2. Vinay applied the distributive property to the equation [tex]$-5(m-2)=25$[/tex]. His equation then became [tex]$-5m+10=-125$[/tex]. Did he apply the distributive property correctly? Explain.

A. Yes. When using the distributive property, you need to multiply all the terms in the equation by the number that is in front of the parentheses.
B. Yes. Vinay multiplied the terms on the left-hand side of the equation by [tex]$-5$[/tex], which is what you are supposed to do.
C. No. Vinay also multiplied the right-hand side of the equation by [tex]$-5$[/tex], which is incorrect.
D. No. The product of [tex]$-5$[/tex] and [tex]$25$[/tex] is [tex]$125$[/tex], not [tex]$-125$[/tex].

Let's examine Vinay's steps and see where he might have gone wrong.

### Original Equation
The original equation is:
[tex]\[ -5(m - 2) = 25 \][/tex]

### Step 1: Apply the Distributive Property
The distributive property states that [tex]$ a(b + c) = ab + ac $[/tex]. So we need to distribute the [tex]$-5$[/tex] to both terms inside the parentheses:
[tex]\[ -5(m - 2) = -5 \cdot m + (-5) \cdot (-2) \][/tex]
Simplifying this, we get:
[tex]\[ -5m + 10 \][/tex]
So, the left-hand side of the equation becomes:
[tex]\[ -5m + 10 \][/tex]

### Step 2: Equate to the Right-Hand Side
After distribution, the equation should still be balanced, equated to the original right-hand side, which is 25:
[tex]\[ -5m + 10 = 25 \][/tex]

### Vinay's Equation
However, Vinay's resulting equation is:
[tex]\[ -5m + 10 = -125 \][/tex]

### Comparing Both Equations
The correct resulting equation from our steps is:
[tex]\[ -5m + 10 = 25 \][/tex]
While Vinay's equation is:
[tex]\[ -5m + 10 = -125 \][/tex]
Clearly, Vinay's resulting equation does not match the correct equation. Therefore, he made a mistake in his work.

### Identifying the Mistake
It looks like Vinay might have tried to multiply the right-hand side of the equation by -5 as well, which is incorrect. The distributive property only applies to the left-hand side within the parentheses, and not to the external result on the right-hand side.

### Conclusion
So, the correct answer is:
[tex]\[ \text{No, Vinay did not apply the distributive property correctly. He incorrectly transformed the right-hand side of the equation.} \][/tex]

The correct application of the distributive property leads to the equation:
[tex]\[ -5m + 10 = 25 \][/tex]