Find the square of 679.

Options

A. 461041
B. 461141
C. 460041
D. 451011

Answer

To find the square of 679, we can use the identity for the square of a binomial, specifically \( (a - b)^2 = a^2 - 2ab + b^2 \). Here, we can express 679 as \( 700 - 21 \).

### Step-by-Step Solution:

1. **Identify \( a \) and \( b \)**:
- Let \( a = 700 \) and \( b = 21 \).
- We need to find \( (700 - 21)^2 \).

2. **Use the binomial square identity**:
- According to the identity \( (a - b)^2 = a^2 - 2ab + b^2 \), we can substitute \( a \) and \( b \):
\[ (700 - 21)^2 = 700^2 - 2 \times 700 \times 21 + 21^2 \]

3. **Calculate \( a^2 \) (which is \( 700^2 \))**:
\[ 700^2 = 490000 \]

4. **Calculate \( b^2 \) (which is \( 21^2 \))**:
\[ 21^2 = 441 \]

5. **Calculate \( 2ab \)**:
\[ 2 \times 700 \times 21 = 29400 \]

6. **Combine the results**:
- Now substitute the values back into the equation:
\[ 679^2 = 490000 + 441 - 29400 \]

7. **Perform the addition and subtraction**:
- First, add \( 490000 + 441 \):
\[ 490000 + 441 = 490441 \]
- Then subtract \( 29400 \):
\[ 490441 - 29400 = 461041 \]

8. **Final Result**:
- Therefore, the square of 679 is:
\[ 679^2 = 461041 \]