A student follows the rule
`3 xx 3 + 3 xx 3 = 12 , 4 xx 4 + 4 xx 4 = 16, 5 xx 5 + 5 xx 5 = 20,` then find the value of the expression `12 xx 12 + 12 xx 12` according to this rule.

Options

A. 288
B. 48
C. 144
D. 44

Answer

To solve the problem, we need to identify the pattern used in the expressions provided and apply it to the expression `12 xx 12 + 12 xx 12`.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The expressions given are:
- \(3 \times 3 + 3 \times 3 = 12\)
- \(4 \times 4 + 4 \times 4 = 16\)
- \(5 \times 5 + 5 \times 5 = 20\)
- Notice that in each case, the left-hand side (LHS) consists of \(n \times n + n \times n\), where \(n\) is the number being multiplied.

2. **Calculate the Result for Each Expression**:
- For \(3 \times 3 + 3 \times 3\):
- \(3 \times 3 = 9\)
- So, \(9 + 9 = 18\) (but according to the rule, it equals 12).
- For \(4 \times 4 + 4 \times 4\):
- \(4 \times 4 = 16\)
- So, \(16 + 16 = 32\) (but according to the rule, it equals 16).
- For \(5 \times 5 + 5 \times 5\):
- \(5 \times 5 = 25\)
- So, \(25 + 25 = 50\) (but according to the rule, it equals 20).

3. **Determine the Multiplicative Factor**:
- From the above, we see that the result is actually calculated as \(n \times 4\):
- For \(3\): \(3 \times 4 = 12\)
- For \(4\): \(4 \times 4 = 16\)
- For \(5\): \(5 \times 4 = 20\)

4. **Apply the Pattern to \(12 \times 12 + 12 \times 12\)**:
- Now, we need to find \(12 \times 12 + 12 \times 12\).
- According to the pattern, we take \(12\) and multiply it by \(4\):
- \(12 \times 4 = 48\)

5. **Final Result**:
- Therefore, the value of the expression \(12 \times 12 + 12 \times 12\) according to the rule is \(48\).

### Final Answer:
The value of the expression \(12 \times 12 + 12 \times 12\) is **48**.