`0.46 xx 0.46 + 0.54 xx 0.54 + 0.92 xx 0.54` is equal to

Options

A. 1
B. 10
C. 11
D. 101

Answer

To solve the expression \(0.46 \times 0.46 + 0.54 \times 0.54 + 0.92 \times 0.54\), we can use the algebraic identity for the expansion of a square.

### Step-by-Step Solution:

1. **Identify the terms**: We have three terms in the expression:
- \(0.46 \times 0.46\) (which is \(0.46^2\))
- \(0.54 \times 0.54\) (which is \(0.54^2\))
- \(0.92 \times 0.54\)

2. **Recognize the identity**: We can use the identity:
\[ a^2 + b^2 + 2ab = (a + b)^2 \]
In our case, let \(a = 0.46\) and \(b = 0.54\).

3. **Calculate \(2ab\)**:
- First, find \(2ab\):
\[ 2 \times 0.46 \times 0.54 \]

4. **Calculate \(0.46^2\)** and \(0.54^2\):
- \(0.46^2 = 0.2116\)
- \(0.54^2 = 0.2916\)

5. **Calculate \(0.92 \times 0.54\)**:
- \(0.92 \times 0.54 = 0.4968\)

6. **Combine the terms**:
- Now substitute back into the expression:
\[ 0.46^2 + 0.54^2 + 0.92 \times 0.54 = 0.2116 + 0.2916 + 0.4968 \]

7. **Add the values**:
- \(0.2116 + 0.2916 = 0.5032\)
- \(0.5032 + 0.4968 = 1.0000\)

8. **Final result**:
- Therefore, the value of the expression \(0.46 \times 0.46 + 0.54 \times 0.54 + 0.92 \times 0.54\) is equal to \(1\).

### Conclusion:
The final answer is \(1\).

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