Verify : `(-50)xx[37+(-7)]=(-50)xx37+(-50)xx(-7)`.

Answer

To verify the equation \((-50) \times [37 + (-7)] = (-50) \times 37 + (-50) \times (-7)\), we will calculate both sides step by step.

### Step 1: Calculate the Left-Hand Side (LHS)
The LHS is given by:
\[ (-50) \times [37 + (-7)] \]
First, we simplify the expression inside the brackets:
\[ 37 + (-7) = 37 - 7 = 30 \]
Now substituting this back into the LHS:
\[ (-50) \times 30 \]
Next, we perform the multiplication:
\[ (-50) \times 30 = -1500 \]
So, the LHS is:
\[ LHS = -1500 \]

### Step 2: Calculate the Right-Hand Side (RHS)
The RHS is given by:
\[ (-50) \times 37 + (-50) \times (-7) \]
We will calculate each term separately.

1. Calculate \((-50) \times 37\):
\[ (-50) \times 37 = -1850 \]

2. Calculate \((-50) \times (-7)\):
\[ (-50) \times (-7) = 350 \quad \text{(since a negative times a negative is positive)} \]

Now we combine these results:
\[ RHS = -1850 + 350 \]

### Step 3: Perform the Addition
Now we perform the addition:
\[ -1850 + 350 = -1500 \]

### Conclusion
Now we compare the LHS and RHS:
\[ LHS = -1500 \quad \text{and} \quad RHS = -1500 \]
Since both sides are equal, we have verified that:
\[ (-50) \times [37 + (-7)] = (-50) \times 37 + (-50) \times (-7) \]

### Final Answer
Thus, the equation is verified:
\[ \text{LHS} = \text{RHS} \]

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