Using distributive law, find the square of 43.

Answer

To find the square of 43 using the distributive law, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Number**:
We can express 43 as the sum of two numbers:
\[ 43 = 40 + 3 \]

2. **Apply the Square Formula**:
According to the formula for squaring a binomial, we have:
\[ (a + b)^2 = a^2 + 2ab + b^2 \]
Here, \(a = 40\) and \(b = 3\). Therefore, we can write:
\[ 43^2 = (40 + 3)^2 = 40^2 + 2 \times 40 \times 3 + 3^2 \]

3. **Calculate Each Term**:
- Calculate \(40^2\):
\[ 40^2 = 1600 \]
- Calculate \(2 \times 40 \times 3\):
\[ 2 \times 40 \times 3 = 240 \]
- Calculate \(3^2\):
\[ 3^2 = 9 \]

4. **Combine the Results**:
Now, we add all the calculated terms together:
\[ 43^2 = 1600 + 240 + 9 \]

5. **Perform the Addition**:
- First, add \(1600\) and \(240\):
\[ 1600 + 240 = 1840 \]
- Then add \(9\):
\[ 1840 + 9 = 1849 \]

6. **Final Result**:
Thus, the square of 43 is:
\[ 43^2 = 1849 \]