`(a +b) ^(2) = a ^(2) + b ^(2)`

Options

A. no
B. yes
C. cannot sure
D. none of the above

Answer

To solve the equation \((a + b)^2 = a^2 + b^2\), we will start by using the algebraic identity for the square of a binomial.

### Step-by-step Solution:

1. **Recall the Identity**:
The identity for the square of a binomial states:
\[ (a + b)^2 = a^2 + b^2 + 2ab \]

2. **Set Up the Equation**:
We start with the given equation:
\[ (a + b)^2 = a^2 + b^2 \]

3. **Substitute the Identity**:
Substitute the identity into the equation:
\[ a^2 + b^2 + 2ab = a^2 + b^2 \]

4. **Simplify the Equation**:
Now, we can subtract \(a^2 + b^2\) from both sides:
\[ 2ab = 0 \]

5. **Solve for \(a\) and \(b\)**:
The equation \(2ab = 0\) implies that either \(a = 0\) or \(b = 0\) (or both). This means:
\[ a = 0 \quad \text{or} \quad b = 0 \]

### Conclusion:
The solution to the equation \((a + b)^2 = a^2 + b^2\) is that either \(a\) or \(b\) must be zero.