Evaluate the following using properties for multiplication to simplify the multiplication.
`34 times (-7)+(-34) times 6`

Answer

To evaluate the expression \( 34 \times (-7) + (-34) \times 6 \) using properties of multiplication, we can follow these steps:

### Step 1: Identify the expression
The expression we need to evaluate is:
\[ 34 \times (-7) + (-34) \times 6 \]

### Step 2: Apply the distributive property
We can factor out the common factor of \(34\) from both terms:
\[ 34 \times (-7) + (-34) \times 6 = 34 \times (-7) + 34 \times (-6) \]
This can be rewritten as:
\[ 34 \times [(-7) + (-6)] \]

### Step 3: Simplify the expression inside the brackets
Now, we simplify the expression inside the brackets:
\[ (-7) + (-6) = -7 - 6 = -13 \]

### Step 4: Substitute back into the expression
Now we substitute back into our expression:
\[ 34 \times (-13) \]

### Step 5: Perform the multiplication
Now, we multiply:
\[ 34 \times (-13) = -442 \]

### Final Answer
Thus, the final result of the expression \( 34 \times (-7) + (-34) \times 6 \) is:
\[ \boxed{-442} \]

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