What is the value of `1.27 times1.27+2.54 times 1.73+1.73 times 1.73.`

Options

A. 9.0146
B. 9.0219
C. 9.1349
D. None of these

Answer

To solve the expression \(1.27 \times 1.27 + 2.54 \times 1.73 + 1.73 \times 1.73\), we can follow these steps:

### Step 1: Identify the components of the expression
We have three terms:
1. \(1.27 \times 1.27\) (which is \(1.27^2\))
2. \(2.54 \times 1.73\)
3. \(1.73 \times 1.73\) (which is \(1.73^2\))

### Step 2: Rewrite the expression
Notice that \(2.54\) can be rewritten as \(2 \times 1.27 \times 1.73\). Thus, we can rewrite the entire expression as:
\[ 1.27^2 + 2 \times 1.27 \times 1.73 + 1.73^2 \]

### Step 3: Recognize the pattern
The expression now resembles the expansion of a square:
\[ a^2 + 2ab + b^2 = (a + b)^2 \]
where \(a = 1.27\) and \(b = 1.73\).

### Step 4: Calculate \(a + b\)
Now, we calculate:
\[ 1.27 + 1.73 = 3.00 \]

### Step 5: Square the sum
Now we square the sum:
\[ (3.00)^2 = 9.00 \]

### Conclusion
Thus, the value of the expression \(1.27 \times 1.27 + 2.54 \times 1.73 + 1.73 \times 1.73\) is \(9.00\).