Verify the distributive law of multiplication over addition :
`(-16)xx{(-5)+(-6)}={(-16)xx(-5)}+{(-16)xx(-6)}`.

Answer

To verify the distributive law of multiplication over addition, we need to show that:

\[ (-16) \times (-5 + -6) = (-16) \times (-5) + (-16) \times (-6) \]

### Step 1: Calculate the Left-Hand Side (LHS)

The LHS is given by:

\[ (-16) \times (-5 + -6) \]

First, we simplify the expression inside the parentheses:

\[ -5 + -6 = -5 - 6 = -11 \]

Now, substituting back into the LHS:

\[ LHS = (-16) \times (-11) \]

Next, we calculate this multiplication:

\[ (-16) \times (-11) = 16 \times 11 = 176 \]

So,

\[ LHS = 176 \]

### Step 2: Calculate the Right-Hand Side (RHS)

The RHS is given by:

\[ (-16) \times (-5) + (-16) \times (-6) \]

Now we calculate each term separately:

1. First term:

\[ (-16) \times (-5) = 16 \times 5 = 80 \]

2. Second term:

\[ (-16) \times (-6) = 16 \times 6 = 96 \]

Now we add these two results together:

\[ RHS = 80 + 96 = 176 \]

### Step 3: Compare LHS and RHS

Now we compare the results of LHS and RHS:

\[ LHS = 176 \quad \text{and} \quad RHS = 176 \]

Since both sides are equal, we have verified the distributive law of multiplication over addition:

\[ (-16) \times (-5 + -6) = (-16) \times (-5) + (-16) \times (-6) \]

### Conclusion

The distributive law of multiplication over addition is valid.

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