Verify and state the property used in each of the following.
`5 times(8 + 5)=(5 times8) + (5 times 5)`

Answer

To verify the equation \(5 \times (8 + 5) = (5 \times 8) + (5 \times 5)\), we will follow these steps:

### Step 1: Calculate the Left-Hand Side (LHS)
We start with the left-hand side of the equation:
\[ LHS = 5 \times (8 + 5) \]
First, we calculate the expression inside the parentheses:
\[ 8 + 5 = 13 \]
Now, we multiply:
\[ 5 \times 13 = 65 \]
Thus, the left-hand side is:
\[ LHS = 65 \]

### Step 2: Calculate the Right-Hand Side (RHS)
Next, we calculate the right-hand side of the equation:
\[ RHS = (5 \times 8) + (5 \times 5) \]
We calculate each multiplication separately:
\[ 5 \times 8 = 40 \]
\[ 5 \times 5 = 25 \]
Now, we add these two results:
\[ 40 + 25 = 65 \]
Thus, the right-hand side is:
\[ RHS = 65 \]

### Step 3: Compare LHS and RHS
Now we compare the results from both sides:
\[ LHS = 65 \quad \text{and} \quad RHS = 65 \]
Since both sides are equal:
\[ LHS = RHS \]
This confirms that the equation is verified.

### Step 4: State the Property Used
The property used in this verification is the **Distributive Property** of multiplication over addition. This property states that:
\[ a \times (b + c) = (a \times b) + (a \times c) \]
In our case, \(a = 5\), \(b = 8\), and \(c = 5\).

### Summary
Thus, we have verified that:
\[ 5 \times (8 + 5) = (5 \times 8) + (5 \times 5) \]
and the property used is the **Distributive Property**.

---