Use the suitable property to simplify each of the following and also name them.
`586xx4+586xx6`

Answer

To simplify the expression \(586 \times 4 + 586 \times 6\), we can follow these steps:

### Step 1: Identify the common factor
In the expression \(586 \times 4 + 586 \times 6\), we can see that \(586\) is a common factor in both terms.

### Step 2: Apply the Distributive Property
Using the distributive property of multiplication, we can factor out the common term \(586\):
\[ 586 \times 4 + 586 \times 6 = 586 \times (4 + 6) \]

### Step 3: Simplify the expression inside the parentheses
Now, we simplify the expression inside the parentheses:
\[ 4 + 6 = 10 \]

### Step 4: Multiply the common factor by the simplified sum
Now we substitute back into the expression:
\[ 586 \times (4 + 6) = 586 \times 10 \]

### Step 5: Calculate the final result
Now we perform the multiplication:
\[ 586 \times 10 = 5860 \]

### Final Answer
Thus, the simplified expression is:
\[ 586 \times 4 + 586 \times 6 = 5860 \]

### Properties Used
The property used in this simplification is called the **Distributive Property of Multiplication**.

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